14
$\begingroup$

Driven by a silly conversation at work, here's the puzzle.

Slack allows users to send emoji as a reaction to a message. Emoji are listed left to right in chronological order of reaction, and 'stacks' emoji in the same place if they're reused for a message, instead of drawing it again.

I want react to every message containing an integer with an emoji sequence that is an equation for that integer.

Number 12 over here can be represented with a sequence of 10 + 2

Given that:

  • I may only use each emoji once
  • I cannot concatenate emoji to make a large number
  • There are no emoji brackets
  • The whole equation must be on one line
  • Correctly evaluate to the input using standard order of operations
  • and that the emoji specification only contains the following maths-related emoji:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, +, /, -, *

or in emoji form:

0️⃣, 1️⃣, 2️⃣, 3️⃣, 4️⃣, 5️⃣, 6️⃣, 7️⃣, 8️⃣, 9️⃣, 🔟, 💯, ➕, ➗, ➖, ✖️

Puzzles / Questions:

  1. What is the smallest positive integer that I will not be able to make an equation for?
  2. What is the largest negative integer that I will not be able to make an equation for?
  3. Is there an algorithm for constructing the formulae, given an input integer?

For fun, and to remove ambiguity, I'll call the numbers that can't be broken down 'emoji-primes'.

$\endgroup$
  • 3
    $\begingroup$ Does normal order of operations apply here, where multiplication/division take precedence over addition/subtraction? Or should the operators always be evaluated left to right? $\endgroup$ – Tonkleton Feb 11 at 19:29
  • $\begingroup$ Hi @Tonkleton - I did this on a guest account and foolishly can't get back to it at the moment. I would say that normal order of operations apply here, no left-to-right evaluation! $\endgroup$ – sjwarner Feb 11 at 20:17
  • $\begingroup$ By "largest negative integer" do you mean largest in absolute value? $\endgroup$ – 2012rcampion Feb 11 at 20:57
  • $\begingroup$ Hi @2012rcampion - I meant largest negative as in negative closest to zero, if that makes sense? Poor choice of words by me, sorry! $\endgroup$ – sjwarner Feb 11 at 21:18
  • $\begingroup$ so you are going to ignore the "chance" to use the blue number (which hold the count of the respective emoji) ? $\endgroup$ – eagle275 Feb 12 at 14:21
4
$\begingroup$

To directly answer your questions:

  1. 211
  2. -201
  3. There is an algorithm to construct the formula for a given integer, but to find all emoji-primes it is more efficient to compute all permutations instead.

I've written a brute force implementation that outputs all possible formulae and emoji-primes: https://github.com/markhobson/emoji-primes

The full results are too long to post here so I've omitted the emoji-primes for brevity:

-1000 = 0️⃣ ➖ 🔟 ✖️ 💯
 -999 = 1️⃣ ➖ 🔟 ✖️ 💯
 -998 = 2️⃣ ➖ 🔟 ✖️ 💯
 -997 = 3️⃣ ➖ 🔟 ✖️ 💯
 -996 = 4️⃣ ➖ 🔟 ✖️ 💯
 -995 = 5️⃣ ➖ 🔟 ✖️ 💯
 -994 = 6️⃣ ➖ 🔟 ✖️ 💯
 -993 = 7️⃣ ➖ 🔟 ✖️ 💯
 -992 = 8️⃣ ➖ 🔟 ✖️ 💯
 -991 = 9️⃣ ➖ 🔟 ✖️ 💯
 -990 = 1️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
 -989 = 2️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
 -988 = 3️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
 -987 = 4️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
 -986 = 5️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
 -985 = 6️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
 -984 = 7️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
 -983 = 8️⃣ ➕ 9️⃣ ➖ 🔟 ✖️ 💯
  ...
 -900 = 0️⃣ ➖ 9️⃣ ✖️ 💯
 -899 = 1️⃣ ➖ 9️⃣ ✖️ 💯
 -898 = 2️⃣ ➖ 9️⃣ ✖️ 💯
 -897 = 3️⃣ ➖ 9️⃣ ✖️ 💯
 -896 = 4️⃣ ➖ 9️⃣ ✖️ 💯
 -895 = 5️⃣ ➖ 9️⃣ ✖️ 💯
 -894 = 6️⃣ ➖ 9️⃣ ✖️ 💯
 -893 = 7️⃣ ➖ 9️⃣ ✖️ 💯
 -892 = 8️⃣ ➖ 9️⃣ ✖️ 💯
 -891 = 1️⃣ ➕ 8️⃣ ➖ 9️⃣ ✖️ 💯
 -890 = 🔟 ➖ 9️⃣ ✖️ 💯
 -889 = 1️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
 -888 = 2️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
 -887 = 3️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
 -886 = 4️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
 -885 = 5️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
 -884 = 6️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
 -883 = 7️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
 -882 = 8️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯
  ...
 -800 = 0️⃣ ➖ 8️⃣ ✖️ 💯
 -799 = 1️⃣ ➖ 8️⃣ ✖️ 💯
 -798 = 2️⃣ ➖ 8️⃣ ✖️ 💯
 -797 = 3️⃣ ➖ 8️⃣ ✖️ 💯
 -796 = 4️⃣ ➖ 8️⃣ ✖️ 💯
 -795 = 5️⃣ ➖ 8️⃣ ✖️ 💯
 -794 = 6️⃣ ➖ 8️⃣ ✖️ 💯
 -793 = 7️⃣ ➖ 8️⃣ ✖️ 💯
 -792 = 1️⃣ ➕ 7️⃣ ➖ 8️⃣ ✖️ 💯
 -791 = 9️⃣ ➖ 8️⃣ ✖️ 💯
 -790 = 🔟 ➖ 8️⃣ ✖️ 💯
 -789 = 1️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
 -788 = 2️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
 -787 = 3️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
 -786 = 4️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
 -785 = 5️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
 -784 = 6️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
 -783 = 7️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
  ...
 -781 = 9️⃣ ➕ 🔟 ➖ 8️⃣ ✖️ 💯
  ...
 -700 = 0️⃣ ➖ 7️⃣ ✖️ 💯
 -699 = 1️⃣ ➖ 7️⃣ ✖️ 💯
 -698 = 2️⃣ ➖ 7️⃣ ✖️ 💯
 -697 = 3️⃣ ➖ 7️⃣ ✖️ 💯
 -696 = 4️⃣ ➖ 7️⃣ ✖️ 💯
 -695 = 5️⃣ ➖ 7️⃣ ✖️ 💯
 -694 = 6️⃣ ➖ 7️⃣ ✖️ 💯
 -693 = 1️⃣ ➕ 6️⃣ ➖ 7️⃣ ✖️ 💯
 -692 = 8️⃣ ➖ 7️⃣ ✖️ 💯
 -691 = 9️⃣ ➖ 7️⃣ ✖️ 💯
 -690 = 🔟 ➖ 7️⃣ ✖️ 💯
 -689 = 1️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
 -688 = 2️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
 -687 = 3️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
 -686 = 4️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
 -685 = 5️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
 -684 = 6️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
 -683 = 8️⃣ ➕ 9️⃣ ➖ 7️⃣ ✖️ 💯
 -682 = 8️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
 -681 = 9️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯
  ...
 -600 = 0️⃣ ➖ 6️⃣ ✖️ 💯
 -599 = 1️⃣ ➖ 6️⃣ ✖️ 💯
 -598 = 2️⃣ ➖ 6️⃣ ✖️ 💯
 -597 = 3️⃣ ➖ 6️⃣ ✖️ 💯
 -596 = 4️⃣ ➖ 6️⃣ ✖️ 💯
 -595 = 5️⃣ ➖ 6️⃣ ✖️ 💯
 -594 = 1️⃣ ➕ 5️⃣ ➖ 6️⃣ ✖️ 💯
 -593 = 7️⃣ ➖ 6️⃣ ✖️ 💯
 -592 = 8️⃣ ➖ 6️⃣ ✖️ 💯
 -591 = 9️⃣ ➖ 6️⃣ ✖️ 💯
 -590 = 🔟 ➖ 6️⃣ ✖️ 💯
 -589 = 1️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
 -588 = 2️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
 -587 = 3️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
 -586 = 4️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
 -585 = 5️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
 -584 = 7️⃣ ➕ 9️⃣ ➖ 6️⃣ ✖️ 💯
 -583 = 7️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
 -582 = 8️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
 -581 = 9️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯
  ...
 -500 = 0️⃣ ➖ 5️⃣ ✖️ 💯
 -499 = 1️⃣ ➖ 5️⃣ ✖️ 💯
 -498 = 2️⃣ ➖ 5️⃣ ✖️ 💯
 -497 = 3️⃣ ➖ 5️⃣ ✖️ 💯
 -496 = 4️⃣ ➖ 5️⃣ ✖️ 💯
 -495 = 1️⃣ ➕ 4️⃣ ➖ 5️⃣ ✖️ 💯
 -494 = 6️⃣ ➖ 5️⃣ ✖️ 💯
 -493 = 7️⃣ ➖ 5️⃣ ✖️ 💯
 -492 = 8️⃣ ➖ 5️⃣ ✖️ 💯
 -491 = 9️⃣ ➖ 5️⃣ ✖️ 💯
 -490 = 🔟 ➖ 5️⃣ ✖️ 💯
 -489 = 1️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
 -488 = 2️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
 -487 = 3️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
 -486 = 4️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
 -485 = 6️⃣ ➕ 9️⃣ ➖ 5️⃣ ✖️ 💯
 -484 = 6️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
 -483 = 7️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
 -482 = 8️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
 -481 = 9️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯
  ...
 -450 = 0️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -449 = 1️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
  ...
 -447 = 3️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -446 = 4️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -445 = 5️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -444 = 6️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -443 = 7️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -442 = 8️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -441 = 1️⃣ ➕ 8️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -440 = 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -439 = 1️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -438 = 4️⃣ ➕ 8️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -437 = 3️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -436 = 4️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -435 = 5️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -434 = 6️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -433 = 7️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
 -432 = 8️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 2️⃣
  ...
 -400 = 0️⃣ ➖ 4️⃣ ✖️ 💯
 -399 = 1️⃣ ➖ 4️⃣ ✖️ 💯
 -398 = 2️⃣ ➖ 4️⃣ ✖️ 💯
 -397 = 3️⃣ ➖ 4️⃣ ✖️ 💯
 -396 = 1️⃣ ➕ 3️⃣ ➖ 4️⃣ ✖️ 💯
 -395 = 5️⃣ ➖ 4️⃣ ✖️ 💯
 -394 = 6️⃣ ➖ 4️⃣ ✖️ 💯
 -393 = 7️⃣ ➖ 4️⃣ ✖️ 💯
 -392 = 8️⃣ ➖ 4️⃣ ✖️ 💯
 -391 = 9️⃣ ➖ 4️⃣ ✖️ 💯
 -390 = 🔟 ➖ 4️⃣ ✖️ 💯
 -389 = 1️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
 -388 = 2️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
 -387 = 3️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
 -386 = 5️⃣ ➕ 9️⃣ ➖ 4️⃣ ✖️ 💯
 -385 = 5️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
 -384 = 6️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
 -383 = 7️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
 -382 = 8️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
 -381 = 9️⃣ ➕ 🔟 ➖ 4️⃣ ✖️ 💯
  ...
 -350 = 0️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -349 = 1️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
  ...
 -347 = 3️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -346 = 4️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -345 = 5️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -344 = 6️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -343 = 1️⃣ ➕ 6️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -342 = 8️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -341 = 9️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -340 = 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -339 = 1️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -338 = 3️⃣ ➕ 9️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -337 = 3️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -336 = 4️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -335 = 5️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -334 = 6️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -333 = 8️⃣ ➕ 9️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -332 = 8️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
 -331 = 9️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 2️⃣
  ...
 -300 = 0️⃣ ➖ 3️⃣ ✖️ 💯
 -299 = 1️⃣ ➖ 3️⃣ ✖️ 💯
 -298 = 2️⃣ ➖ 3️⃣ ✖️ 💯
 -297 = 1️⃣ ➕ 2️⃣ ➖ 3️⃣ ✖️ 💯
 -296 = 4️⃣ ➖ 3️⃣ ✖️ 💯
 -295 = 5️⃣ ➖ 3️⃣ ✖️ 💯
 -294 = 6️⃣ ➖ 3️⃣ ✖️ 💯
 -293 = 7️⃣ ➖ 3️⃣ ✖️ 💯
 -292 = 8️⃣ ➖ 3️⃣ ✖️ 💯
 -291 = 9️⃣ ➖ 3️⃣ ✖️ 💯
 -290 = 🔟 ➖ 3️⃣ ✖️ 💯
 -289 = 1️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
 -288 = 2️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
 -287 = 4️⃣ ➕ 9️⃣ ➖ 3️⃣ ✖️ 💯
 -286 = 4️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
 -285 = 5️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
 -284 = 6️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
 -283 = 7️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
 -282 = 8️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
 -281 = 9️⃣ ➕ 🔟 ➖ 3️⃣ ✖️ 💯
  ...
 -250 = 0️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -249 = 1️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -248 = 2️⃣ ➖ 🔟 ✖️ 💯 ➗ 4️⃣
 -247 = 3️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -246 = 4️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -245 = 5️⃣ ➖ 🔟 ✖️ 💯 ➗ 4️⃣
 -244 = 6️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -243 = 7️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -242 = 8️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -241 = 9️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -240 = 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -239 = 1️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -238 = 3️⃣ ➕ 9️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -237 = 3️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -236 = 4️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -235 = 6️⃣ ➕ 9️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -234 = 6️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -233 = 7️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -232 = 8️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
 -231 = 9️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 2️⃣
  ...
 -225 = 0️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -224 = 1️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -223 = 2️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -222 = 3️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -221 = 1️⃣ ➕ 3️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -220 = 5️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -219 = 6️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -218 = 7️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -217 = 8️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -216 = 1️⃣ ➕ 8️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -215 = 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -214 = 1️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -213 = 2️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -212 = 3️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -211 = 6️⃣ ➕ 8️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -210 = 5️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -209 = 6️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -208 = 7️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
 -207 = 8️⃣ ➕ 🔟 ➖ 9️⃣ ✖️ 💯 ➗ 4️⃣
  ...
 -200 = 0️⃣ ➖ 2️⃣ ✖️ 💯
 -199 = 1️⃣ ➖ 2️⃣ ✖️ 💯
 -198 = 2️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 3️⃣
 -197 = 3️⃣ ➖ 2️⃣ ✖️ 💯
 -196 = 4️⃣ ➖ 2️⃣ ✖️ 💯
 -195 = 5️⃣ ➖ 2️⃣ ✖️ 💯
 -194 = 6️⃣ ➖ 2️⃣ ✖️ 💯
 -193 = 7️⃣ ➖ 2️⃣ ✖️ 💯
 -192 = 8️⃣ ➖ 2️⃣ ✖️ 💯
 -191 = 9️⃣ ➖ 2️⃣ ✖️ 💯
 -190 = 🔟 ➖ 2️⃣ ✖️ 💯
 -189 = 1️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -188 = 3️⃣ ➕ 9️⃣ ➖ 2️⃣ ✖️ 💯
 -187 = 3️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -186 = 4️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -185 = 5️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -184 = 6️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -183 = 7️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -182 = 8️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -181 = 9️⃣ ➕ 🔟 ➖ 2️⃣ ✖️ 💯
 -180 = 0️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 5️⃣
 -179 = 1️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 5️⃣
 -178 = 2️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 5️⃣
 -177 = 3️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 5️⃣
 -176 = 4️⃣ ➖ 9️⃣ ✖️ 💯 ➗ 5️⃣
 -175 = 0️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -174 = 1️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -173 = 2️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -172 = 3️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -171 = 1️⃣ ➕ 3️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -170 = 5️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -169 = 6️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -168 = 1️⃣ ➕ 6️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -167 = 8️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -166 = 9️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -165 = 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -164 = 1️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -163 = 2️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -162 = 3️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -161 = 5️⃣ ➕ 9️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 4️⃣
 -160 = 0️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -159 = 1️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -158 = 2️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -157 = 3️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -156 = 4️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -155 = 1️⃣ ➕ 4️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -154 = 6️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -153 = 7️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -152 = 1️⃣ ➕ 7️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -151 = 9️⃣ ➖ 8️⃣ ✖️ 💯 ➗ 5️⃣
 -150 = 0️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -149 = 1️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -148 = 2️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 4️⃣
 -147 = 3️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 4️⃣
 -146 = 4️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -145 = 5️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -144 = 6️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -143 = 7️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -142 = 8️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -141 = 9️⃣ ➖ 3️⃣ ✖️ 💯 ➗ 2️⃣
 -140 = 0️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -139 = 1️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -138 = 2️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -137 = 3️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -136 = 4️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -135 = 1️⃣ ➕ 4️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -134 = 6️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -133 = 1️⃣ ➕ 6️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -132 = 8️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -131 = 9️⃣ ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -130 = 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -129 = 1️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -128 = 2️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -127 = 3️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -126 = 4️⃣ ➕ 🔟 ➖ 7️⃣ ✖️ 💯 ➗ 5️⃣
 -125 = 0️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 4️⃣
 -124 = 1️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 4️⃣
 -123 = 2️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 4️⃣
 -122 = 3️⃣ ➖ 5️⃣ ✖️ 💯 ➗ 4️⃣
 -121 = 4️⃣ ➖ 🔟 ✖️ 💯 ➗ 8️⃣
 -120 = 0️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -119 = 1️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -118 = 2️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -117 = 3️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -116 = 4️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -115 = 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 4️⃣
 -114 = 1️⃣ ➕ 🔟 ➖ 5️⃣ ✖️ 💯 ➗ 4️⃣
 -113 = 7️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -112 = 8️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -111 = 9️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -110 = 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -109 = 1️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -108 = 2️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -107 = 3️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -106 = 4️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -105 = 7️⃣ ➕ 8️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -104 = 7️⃣ ➕ 9️⃣ ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -103 = 7️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -102 = 8️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -101 = 9️⃣ ➕ 🔟 ➖ 6️⃣ ✖️ 💯 ➗ 5️⃣
 -100 = 0️⃣ ➖ 💯
  -99 = 1️⃣ ➖ 💯
  -98 = 2️⃣ ➖ 💯
  -97 = 3️⃣ ➖ 💯
  -96 = 4️⃣ ➖ 💯
  -95 = 5️⃣ ➖ 💯
  -94 = 6️⃣ ➖ 💯
  -93 = 7️⃣ ➖ 💯
  -92 = 8️⃣ ➖ 💯
  -91 = 9️⃣ ➖ 💯
  -90 = 🔟 ➖ 💯
  -89 = 1️⃣ ➕ 🔟 ➖ 💯
  -88 = 2️⃣ ➕ 🔟 ➖ 💯
  -87 = 3️⃣ ➕ 🔟 ➖ 💯
  -86 = 2️⃣ ✖️ 7️⃣ ➖ 💯
  -85 = 3️⃣ ✖️ 5️⃣ ➖ 💯
  -84 = 2️⃣ ✖️ 8️⃣ ➖ 💯
  -83 = 7️⃣ ➕ 🔟 ➖ 💯
  -82 = 2️⃣ ✖️ 9️⃣ ➖ 💯
  -81 = 9️⃣ ➕ 🔟 ➖ 💯
  -80 = 0️⃣ ➖ 8️⃣ ✖️ 🔟
  -79 = 1️⃣ ➖ 8️⃣ ✖️ 🔟
  -78 = 2️⃣ ➖ 8️⃣ ✖️ 🔟
  -77 = 3️⃣ ➖ 8️⃣ ✖️ 🔟
  -76 = 3️⃣ ✖️ 8️⃣ ➖ 💯
  -75 = 5️⃣ ➖ 8️⃣ ✖️ 🔟
  -74 = 6️⃣ ➖ 8️⃣ ✖️ 🔟
  -73 = 3️⃣ ✖️ 9️⃣ ➖ 💯
  -72 = 0️⃣ ➖ 8️⃣ ✖️ 9️⃣
  -71 = 1️⃣ ➖ 8️⃣ ✖️ 9️⃣
  -70 = 0️⃣ ➖ 7️⃣ ✖️ 🔟
  -69 = 1️⃣ ➖ 7️⃣ ✖️ 🔟
  -68 = 2️⃣ ➖ 7️⃣ ✖️ 🔟
  -67 = 3️⃣ ➖ 7️⃣ ✖️ 🔟
  -66 = 4️⃣ ➖ 7️⃣ ✖️ 🔟
  -65 = 5️⃣ ➖ 7️⃣ ✖️ 🔟
  -64 = 4️⃣ ✖️ 9️⃣ ➖ 💯
  -63 = 0️⃣ ➖ 7️⃣ ✖️ 9️⃣
  -62 = 1️⃣ ➖ 7️⃣ ✖️ 9️⃣
  -61 = 2️⃣ ➖ 7️⃣ ✖️ 9️⃣
  -60 = 0️⃣ ➖ 6️⃣ ✖️ 🔟
  -59 = 1️⃣ ➖ 6️⃣ ✖️ 🔟
  -58 = 2️⃣ ➖ 6️⃣ ✖️ 🔟
  -57 = 3️⃣ ➖ 6️⃣ ✖️ 🔟
  -56 = 0️⃣ ➖ 7️⃣ ✖️ 8️⃣
  -55 = 1️⃣ ➖ 7️⃣ ✖️ 8️⃣
  -54 = 0️⃣ ➖ 6️⃣ ✖️ 9️⃣
  -53 = 1️⃣ ➖ 6️⃣ ✖️ 9️⃣
  -52 = 2️⃣ ➖ 6️⃣ ✖️ 9️⃣
  -51 = 3️⃣ ➖ 6️⃣ ✖️ 9️⃣
  -50 = 0️⃣ ➖ 5️⃣ ✖️ 🔟
  -49 = 1️⃣ ➖ 5️⃣ ✖️ 🔟
  -48 = 0️⃣ ➖ 6️⃣ ✖️ 8️⃣
  -47 = 1️⃣ ➖ 6️⃣ ✖️ 8️⃣
  -46 = 2️⃣ ➖ 6️⃣ ✖️ 8️⃣
  -45 = 0️⃣ ➖ 5️⃣ ✖️ 9️⃣
  -44 = 1️⃣ ➖ 5️⃣ ✖️ 9️⃣
  -43 = 2️⃣ ➖ 5️⃣ ✖️ 9️⃣
  -42 = 0️⃣ ➖ 6️⃣ ✖️ 7️⃣
  -41 = 1️⃣ ➖ 6️⃣ ✖️ 7️⃣
  -40 = 0️⃣ ➖ 4️⃣ ✖️ 🔟
  -39 = 1️⃣ ➖ 4️⃣ ✖️ 🔟
  -38 = 2️⃣ ➖ 4️⃣ ✖️ 🔟
  -37 = 3️⃣ ➖ 4️⃣ ✖️ 🔟
  -36 = 0️⃣ ➖ 4️⃣ ✖️ 9️⃣
  -35 = 0️⃣ ➖ 5️⃣ ✖️ 7️⃣
  -34 = 1️⃣ ➖ 5️⃣ ✖️ 7️⃣
  -33 = 2️⃣ ➖ 5️⃣ ✖️ 7️⃣
  -32 = 0️⃣ ➖ 4️⃣ ✖️ 8️⃣
  -31 = 1️⃣ ➖ 4️⃣ ✖️ 8️⃣
  -30 = 0️⃣ ➖ 3️⃣ ✖️ 🔟
  -29 = 1️⃣ ➖ 3️⃣ ✖️ 🔟
  -28 = 0️⃣ ➖ 4️⃣ ✖️ 7️⃣
  -27 = 0️⃣ ➖ 3️⃣ ✖️ 9️⃣
  -26 = 1️⃣ ➖ 3️⃣ ✖️ 9️⃣
  -25 = 0️⃣ ➖ 💯 ➗ 4️⃣
  -24 = 0️⃣ ➖ 3️⃣ ✖️ 8️⃣
  -23 = 1️⃣ ➖ 3️⃣ ✖️ 8️⃣
  -22 = 2️⃣ ➖ 3️⃣ ✖️ 8️⃣
  -21 = 0️⃣ ➖ 3️⃣ ✖️ 7️⃣
  -20 = 0️⃣ ➖ 2️⃣ ✖️ 🔟
  -19 = 1️⃣ ➖ 2️⃣ ✖️ 🔟
  -18 = 0️⃣ ➖ 2️⃣ ✖️ 9️⃣
  -17 = 1️⃣ ➖ 2️⃣ ✖️ 9️⃣
  -16 = 0️⃣ ➖ 2️⃣ ✖️ 8️⃣
  -15 = 0️⃣ ➖ 3️⃣ ✖️ 5️⃣
  -14 = 0️⃣ ➖ 2️⃣ ✖️ 7️⃣
  -13 = 1️⃣ ➖ 2️⃣ ✖️ 7️⃣
  -12 = 0️⃣ ➖ 2️⃣ ✖️ 6️⃣
  -11 = 1️⃣ ➖ 2️⃣ ✖️ 6️⃣
  -10 = 0️⃣ ➖ 🔟
   -9 = 0️⃣ ➖ 9️⃣
   -8 = 0️⃣ ➖ 8️⃣
   -7 = 0️⃣ ➖ 7️⃣
   -6 = 0️⃣ ➖ 6️⃣
   -5 = 0️⃣ ➖ 5️⃣
   -4 = 0️⃣ ➖ 4️⃣
   -3 = 0️⃣ ➖ 3️⃣
   -2 = 0️⃣ ➖ 2️⃣
   -1 = 0️⃣ ➖ 1️⃣
    0 = 0️⃣
    1 = 1️⃣
    2 = 2️⃣
    3 = 3️⃣
    4 = 4️⃣
    5 = 5️⃣
    6 = 6️⃣
    7 = 7️⃣
    8 = 8️⃣
    9 = 9️⃣
   10 = 🔟
   11 = 1️⃣ ➕ 🔟
   12 = 2️⃣ ➕ 🔟
   13 = 3️⃣ ➕ 🔟
   14 = 2️⃣ ✖️ 7️⃣
   15 = 3️⃣ ✖️ 5️⃣
   16 = 2️⃣ ✖️ 8️⃣
   17 = 7️⃣ ➕ 🔟
   18 = 2️⃣ ✖️ 9️⃣
   19 = 9️⃣ ➕ 🔟
   20 = 2️⃣ ✖️ 🔟
   21 = 3️⃣ ✖️ 7️⃣
   22 = 1️⃣ ➕ 3️⃣ ✖️ 7️⃣
   23 = 2️⃣ ➕ 3️⃣ ✖️ 7️⃣
   24 = 3️⃣ ✖️ 8️⃣
   25 = 💯 ➗ 4️⃣
   26 = 1️⃣ ➕ 💯 ➗ 4️⃣
   27 = 3️⃣ ✖️ 9️⃣
   28 = 4️⃣ ✖️ 7️⃣
   29 = 1️⃣ ➕ 4️⃣ ✖️ 7️⃣
   30 = 3️⃣ ✖️ 🔟
   31 = 1️⃣ ➕ 3️⃣ ✖️ 🔟
   32 = 4️⃣ ✖️ 8️⃣
   33 = 1️⃣ ➕ 4️⃣ ✖️ 8️⃣
   34 = 2️⃣ ➕ 4️⃣ ✖️ 8️⃣
   35 = 5️⃣ ✖️ 7️⃣
   36 = 4️⃣ ✖️ 9️⃣
   37 = 1️⃣ ➕ 4️⃣ ✖️ 9️⃣
   38 = 2️⃣ ➕ 4️⃣ ✖️ 9️⃣
   39 = 3️⃣ ➕ 4️⃣ ✖️ 9️⃣
   40 = 4️⃣ ✖️ 🔟
   41 = 1️⃣ ➕ 4️⃣ ✖️ 🔟
   42 = 6️⃣ ✖️ 7️⃣
   43 = 1️⃣ ➕ 6️⃣ ✖️ 7️⃣
   44 = 2️⃣ ➕ 6️⃣ ✖️ 7️⃣
   45 = 5️⃣ ✖️ 9️⃣
   46 = 1️⃣ ➕ 5️⃣ ✖️ 9️⃣
   47 = 2️⃣ ➕ 5️⃣ ✖️ 9️⃣
   48 = 6️⃣ ✖️ 8️⃣
   49 = 1️⃣ ➕ 6️⃣ ✖️ 8️⃣
   50 = 5️⃣ ✖️ 🔟
   51 = 1️⃣ ➕ 5️⃣ ✖️ 🔟
   52 = 2️⃣ ➕ 5️⃣ ✖️ 🔟
   53 = 3️⃣ ➕ 5️⃣ ✖️ 🔟
   54 = 6️⃣ ✖️ 9️⃣
   55 = 1️⃣ ➕ 6️⃣ ✖️ 9️⃣
   56 = 7️⃣ ✖️ 8️⃣
   57 = 1️⃣ ➕ 7️⃣ ✖️ 8️⃣
   58 = 2️⃣ ➕ 7️⃣ ✖️ 8️⃣
   59 = 3️⃣ ➕ 7️⃣ ✖️ 8️⃣
   60 = 6️⃣ ✖️ 🔟
   61 = 1️⃣ ➕ 6️⃣ ✖️ 🔟
   62 = 2️⃣ ➕ 6️⃣ ✖️ 🔟
   63 = 7️⃣ ✖️ 9️⃣
   64 = 1️⃣ ➕ 7️⃣ ✖️ 9️⃣
   65 = 2️⃣ ➕ 7️⃣ ✖️ 9️⃣
   66 = 3️⃣ ➕ 7️⃣ ✖️ 9️⃣
   67 = 4️⃣ ➕ 7️⃣ ✖️ 9️⃣
   68 = 5️⃣ ➕ 7️⃣ ✖️ 9️⃣
   69 = 6️⃣ ➕ 7️⃣ ✖️ 9️⃣
   70 = 7️⃣ ✖️ 🔟
   71 = 1️⃣ ➕ 7️⃣ ✖️ 🔟
   72 = 8️⃣ ✖️ 9️⃣
   73 = 1️⃣ ➕ 8️⃣ ✖️ 9️⃣
   74 = 2️⃣ ➕ 8️⃣ ✖️ 9️⃣
   75 = 3️⃣ ➕ 8️⃣ ✖️ 9️⃣
   76 = 4️⃣ ➕ 8️⃣ ✖️ 9️⃣
   77 = 5️⃣ ➕ 8️⃣ ✖️ 9️⃣
   78 = 6️⃣ ➕ 8️⃣ ✖️ 9️⃣
   79 = 7️⃣ ➕ 8️⃣ ✖️ 9️⃣
   80 = 8️⃣ ✖️ 🔟
   81 = 1️⃣ ➕ 8️⃣ ✖️ 🔟
   82 = 2️⃣ ➕ 8️⃣ ✖️ 🔟
   83 = 3️⃣ ➕ 8️⃣ ✖️ 🔟
   84 = 4️⃣ ➕ 8️⃣ ✖️ 🔟
   85 = 5️⃣ ➕ 8️⃣ ✖️ 🔟
   86 = 6️⃣ ➕ 8️⃣ ✖️ 🔟
   87 = 7️⃣ ➕ 8️⃣ ✖️ 🔟
   88 = 9️⃣ ✖️ 🔟 ➖ 2️⃣
   89 = 8️⃣ ✖️ 🔟 ➕ 9️⃣
   90 = 9️⃣ ✖️ 🔟
   91 = 💯 ➖ 9️⃣
   92 = 💯 ➖ 8️⃣
   93 = 💯 ➖ 7️⃣
   94 = 💯 ➖ 6️⃣
   95 = 💯 ➖ 5️⃣
   96 = 💯 ➖ 4️⃣
   97 = 💯 ➖ 3️⃣
   98 = 💯 ➖ 2️⃣
   99 = 💯 ➖ 1️⃣
  100 = 💯
  101 = 1️⃣ ➕ 💯
  102 = 2️⃣ ➕ 💯
  103 = 3️⃣ ➕ 💯
  104 = 4️⃣ ➕ 💯
  105 = 5️⃣ ➕ 💯
  106 = 6️⃣ ➕ 💯
  107 = 7️⃣ ➕ 💯
  108 = 8️⃣ ➕ 💯
  109 = 9️⃣ ➕ 💯
  110 = 🔟 ➕ 💯
  111 = 2️⃣ ✖️ 6️⃣ ➕ 💯 ➖ 1️⃣
  112 = 2️⃣ ✖️ 6️⃣ ➕ 💯
  113 = 2️⃣ ✖️ 7️⃣ ➕ 💯 ➖ 1️⃣
  114 = 2️⃣ ✖️ 7️⃣ ➕ 💯
  115 = 3️⃣ ✖️ 5️⃣ ➕ 💯
  116 = 2️⃣ ✖️ 8️⃣ ➕ 💯
  117 = 2️⃣ ✖️ 9️⃣ ➕ 💯 ➖ 1️⃣
  118 = 2️⃣ ✖️ 9️⃣ ➕ 💯
  119 = 2️⃣ ✖️ 🔟 ➕ 💯 ➖ 1️⃣
  120 = 2️⃣ ✖️ 🔟 ➕ 💯
  121 = 3️⃣ ✖️ 7️⃣ ➕ 💯
  122 = 2️⃣ ➕ 6️⃣ ✖️ 💯 ➗ 5️⃣
  123 = 3️⃣ ➕ 6️⃣ ✖️ 💯 ➗ 5️⃣
  124 = 3️⃣ ✖️ 8️⃣ ➕ 💯
  125 = 5️⃣ ✖️ 💯 ➗ 4️⃣
  126 = 1️⃣ ➕ 5️⃣ ✖️ 💯 ➗ 4️⃣
  127 = 3️⃣ ✖️ 9️⃣ ➕ 💯
  128 = 4️⃣ ✖️ 7️⃣ ➕ 💯
  129 = 3️⃣ ✖️ 🔟 ➕ 💯 ➖ 1️⃣
  130 = 3️⃣ ✖️ 🔟 ➕ 💯
  131 = 4️⃣ ✖️ 8️⃣ ➕ 💯 ➖ 1️⃣
  132 = 4️⃣ ✖️ 8️⃣ ➕ 💯
  133 = 4️⃣ ✖️ 9️⃣ ➕ 💯 ➖ 3️⃣
  134 = 4️⃣ ✖️ 9️⃣ ➕ 💯 ➖ 2️⃣
  135 = 5️⃣ ✖️ 7️⃣ ➕ 💯
  136 = 4️⃣ ✖️ 9️⃣ ➕ 💯
  137 = 4️⃣ ✖️ 🔟 ➕ 💯 ➖ 3️⃣
  138 = 4️⃣ ✖️ 🔟 ➕ 💯 ➖ 2️⃣
  139 = 4️⃣ ✖️ 🔟 ➕ 💯 ➖ 1️⃣
  140 = 4️⃣ ✖️ 🔟 ➕ 💯
  141 = 1️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 5️⃣
  142 = 6️⃣ ✖️ 7️⃣ ➕ 💯
  143 = 3️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 5️⃣
  144 = 3️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 6️⃣
  145 = 5️⃣ ✖️ 9️⃣ ➕ 💯
  146 = 3️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 4️⃣
  147 = 5️⃣ ✖️ 🔟 ➕ 💯 ➖ 3️⃣
  148 = 6️⃣ ✖️ 8️⃣ ➕ 💯
  149 = 3️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 1️⃣
  150 = 3️⃣ ✖️ 💯 ➗ 2️⃣
  151 = 1️⃣ ➕ 3️⃣ ✖️ 💯 ➗ 2️⃣
  152 = 2️⃣ ➕ 6️⃣ ✖️ 💯 ➗ 4️⃣
  153 = 3️⃣ ➕ 6️⃣ ✖️ 💯 ➗ 4️⃣
  154 = 6️⃣ ✖️ 9️⃣ ➕ 💯
  155 = 3️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 5️⃣
  156 = 7️⃣ ✖️ 8️⃣ ➕ 💯
  157 = 3️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 7️⃣
  158 = 3️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 8️⃣
  159 = 3️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 9️⃣
  160 = 6️⃣ ✖️ 🔟 ➕ 💯
  161 = 1️⃣ ➕ 8️⃣ ✖️ 💯 ➗ 5️⃣
  162 = 2️⃣ ➕ 8️⃣ ✖️ 💯 ➗ 5️⃣
  163 = 7️⃣ ✖️ 9️⃣ ➕ 💯
  164 = 4️⃣ ➕ 8️⃣ ✖️ 💯 ➗ 5️⃣
  165 = 7️⃣ ✖️ 🔟 ➕ 💯 ➖ 5️⃣
  166 = 6️⃣ ➕ 8️⃣ ✖️ 💯 ➗ 5️⃣
  167 = 7️⃣ ➕ 8️⃣ ✖️ 💯 ➗ 5️⃣
  168 = 7️⃣ ✖️ 🔟 ➕ 💯 ➖ 2️⃣
  169 = 7️⃣ ✖️ 🔟 ➕ 💯 ➖ 1️⃣
  170 = 7️⃣ ✖️ 🔟 ➕ 💯
  171 = 8️⃣ ✖️ 9️⃣ ➕ 💯 ➖ 1️⃣
  172 = 8️⃣ ✖️ 9️⃣ ➕ 💯
  173 = 7️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 2️⃣
  174 = 7️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 1️⃣
  175 = 7️⃣ ✖️ 💯 ➗ 4️⃣
  176 = 1️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 4️⃣
  177 = 2️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 4️⃣
  178 = 3️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 4️⃣
  179 = 8️⃣ ✖️ 🔟 ➕ 💯 ➖ 1️⃣
  180 = 8️⃣ ✖️ 🔟 ➕ 💯
  181 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 5️⃣
  182 = 2️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 5️⃣
  183 = 3️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 5️⃣
  184 = 4️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 5️⃣
  185 = 7️⃣ ✖️ 💯 ➗ 4️⃣ ➕ 🔟
  186 = 6️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 5️⃣
  187 = 7️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 5️⃣
  188 = 8️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 5️⃣
  189 = 9️⃣ ✖️ 🔟 ➕ 💯 ➖ 1️⃣
  190 = 2️⃣ ✖️ 💯 ➖ 🔟
  191 = 2️⃣ ✖️ 💯 ➖ 9️⃣
  192 = 2️⃣ ✖️ 💯 ➖ 8️⃣
  193 = 2️⃣ ✖️ 💯 ➖ 7️⃣
  194 = 2️⃣ ✖️ 💯 ➖ 6️⃣
  195 = 2️⃣ ✖️ 💯 ➖ 5️⃣
  196 = 2️⃣ ✖️ 💯 ➖ 4️⃣
  197 = 2️⃣ ✖️ 💯 ➖ 3️⃣
  198 = 1️⃣ ➕ 2️⃣ ✖️ 💯 ➖ 3️⃣
  199 = 2️⃣ ✖️ 💯 ➖ 1️⃣
  200 = 2️⃣ ✖️ 💯
  201 = 1️⃣ ➕ 2️⃣ ✖️ 💯
  202 = 2️⃣ ➕ 6️⃣ ✖️ 💯 ➗ 3️⃣
  203 = 2️⃣ ✖️ 💯 ➕ 3️⃣
  204 = 2️⃣ ✖️ 💯 ➕ 4️⃣
  205 = 2️⃣ ✖️ 💯 ➕ 5️⃣
  206 = 2️⃣ ✖️ 💯 ➕ 6️⃣
  207 = 2️⃣ ✖️ 💯 ➕ 7️⃣
  208 = 2️⃣ ✖️ 💯 ➕ 8️⃣
  209 = 2️⃣ ✖️ 💯 ➕ 9️⃣
  210 = 2️⃣ ✖️ 💯 ➕ 🔟
  ...
  215 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 🔟
  216 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 🔟
  217 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 8️⃣
  218 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 7️⃣
  219 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 6️⃣
  220 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 5️⃣
  221 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 5️⃣
  222 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 3️⃣
  223 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 2️⃣
  224 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 1️⃣
  225 = 9️⃣ ✖️ 💯 ➗ 4️⃣
  226 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣
  227 = 2️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣
  228 = 3️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣
  229 = 5️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣ ➖ 1️⃣
  230 = 5️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣
  231 = 6️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣
  232 = 7️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣
  233 = 8️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 4️⃣
  234 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➕ 🔟 ➖ 1️⃣
  235 = 9️⃣ ✖️ 💯 ➗ 4️⃣ ➕ 🔟
  ...
  240 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 🔟
  241 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 9️⃣
  242 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 8️⃣
  243 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 7️⃣
  244 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 6️⃣
  245 = 🔟 ✖️ 💯 ➗ 4️⃣ ➖ 5️⃣
  246 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 4️⃣
  247 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 3️⃣
  248 = 🔟 ✖️ 💯 ➗ 4️⃣ ➖ 2️⃣
  249 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 1️⃣
  250 = 5️⃣ ✖️ 💯 ➗ 2️⃣
  251 = 1️⃣ ➕ 5️⃣ ✖️ 💯 ➗ 2️⃣
  252 = 2️⃣ ➕ 🔟 ✖️ 💯 ➗ 4️⃣
  253 = 3️⃣ ➕ 5️⃣ ✖️ 💯 ➗ 2️⃣
  254 = 4️⃣ ➕ 5️⃣ ✖️ 💯 ➗ 2️⃣
  255 = 5️⃣ ➕ 🔟 ✖️ 💯 ➗ 4️⃣
  256 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 6️⃣
  257 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 7️⃣
  258 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 8️⃣
  259 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 9️⃣
  260 = 5️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 🔟
  ...
  290 = 3️⃣ ✖️ 💯 ➖ 🔟
  291 = 3️⃣ ✖️ 💯 ➖ 9️⃣
  292 = 3️⃣ ✖️ 💯 ➖ 8️⃣
  293 = 3️⃣ ✖️ 💯 ➖ 7️⃣
  294 = 3️⃣ ✖️ 💯 ➖ 6️⃣
  295 = 3️⃣ ✖️ 💯 ➖ 5️⃣
  296 = 3️⃣ ✖️ 💯 ➖ 4️⃣
  297 = 1️⃣ ➕ 3️⃣ ✖️ 💯 ➖ 4️⃣
  298 = 3️⃣ ✖️ 💯 ➖ 2️⃣
  299 = 3️⃣ ✖️ 💯 ➖ 1️⃣
  300 = 3️⃣ ✖️ 💯
  301 = 1️⃣ ➕ 3️⃣ ✖️ 💯
  302 = 2️⃣ ➕ 3️⃣ ✖️ 💯
  303 = 3️⃣ ➕ 6️⃣ ✖️ 💯 ➗ 2️⃣
  304 = 3️⃣ ✖️ 💯 ➕ 4️⃣
  305 = 3️⃣ ✖️ 💯 ➕ 5️⃣
  306 = 3️⃣ ✖️ 💯 ➕ 6️⃣
  307 = 3️⃣ ✖️ 💯 ➕ 7️⃣
  308 = 3️⃣ ✖️ 💯 ➕ 8️⃣
  309 = 3️⃣ ✖️ 💯 ➕ 9️⃣
  310 = 3️⃣ ✖️ 💯 ➕ 🔟
  ...
  340 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 🔟
  341 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 9️⃣
  342 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 8️⃣
  343 = 1️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 8️⃣
  344 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 6️⃣
  345 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 5️⃣
  346 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 4️⃣
  347 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 3️⃣
  348 = 1️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 3️⃣
  349 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 1️⃣
  350 = 7️⃣ ✖️ 💯 ➗ 2️⃣
  351 = 1️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣
  352 = 3️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 1️⃣
  353 = 3️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣
  354 = 4️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣
  355 = 5️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣
  356 = 6️⃣ ➕ 7️⃣ ✖️ 💯 ➗ 2️⃣
  357 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 8️⃣ ➖ 1️⃣
  358 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 8️⃣
  359 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 9️⃣
  360 = 7️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 🔟
  ...
  390 = 4️⃣ ✖️ 💯 ➖ 🔟
  391 = 4️⃣ ✖️ 💯 ➖ 9️⃣
  392 = 4️⃣ ✖️ 💯 ➖ 8️⃣
  393 = 4️⃣ ✖️ 💯 ➖ 7️⃣
  394 = 4️⃣ ✖️ 💯 ➖ 6️⃣
  395 = 4️⃣ ✖️ 💯 ➖ 5️⃣
  396 = 1️⃣ ➕ 4️⃣ ✖️ 💯 ➖ 5️⃣
  397 = 4️⃣ ✖️ 💯 ➖ 3️⃣
  398 = 4️⃣ ✖️ 💯 ➖ 2️⃣
  399 = 4️⃣ ✖️ 💯 ➖ 1️⃣
  400 = 4️⃣ ✖️ 💯
  401 = 1️⃣ ➕ 4️⃣ ✖️ 💯
  402 = 2️⃣ ➕ 4️⃣ ✖️ 💯
  403 = 3️⃣ ➕ 4️⃣ ✖️ 💯
  404 = 4️⃣ ➕ 8️⃣ ✖️ 💯 ➗ 2️⃣
  405 = 4️⃣ ✖️ 💯 ➕ 5️⃣
  406 = 4️⃣ ✖️ 💯 ➕ 6️⃣
  407 = 4️⃣ ✖️ 💯 ➕ 7️⃣
  408 = 4️⃣ ✖️ 💯 ➕ 8️⃣
  409 = 4️⃣ ✖️ 💯 ➕ 9️⃣
  410 = 4️⃣ ✖️ 💯 ➕ 🔟
  ...
  440 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 🔟
  441 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 🔟
  442 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 8️⃣
  443 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 7️⃣
  444 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 6️⃣
  445 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 5️⃣
  446 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 4️⃣
  447 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 3️⃣
  448 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 3️⃣
  449 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 1️⃣
  450 = 9️⃣ ✖️ 💯 ➗ 2️⃣
  451 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣
  452 = 3️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣ ➖ 1️⃣
  453 = 3️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣
  454 = 4️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣
  455 = 5️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣
  456 = 6️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣
  457 = 7️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣
  458 = 8️⃣ ➕ 9️⃣ ✖️ 💯 ➗ 2️⃣
  459 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 🔟 ➖ 1️⃣
  460 = 9️⃣ ✖️ 💯 ➗ 2️⃣ ➕ 🔟
  ...
  490 = 5️⃣ ✖️ 💯 ➖ 🔟
  491 = 5️⃣ ✖️ 💯 ➖ 9️⃣
  492 = 5️⃣ ✖️ 💯 ➖ 8️⃣
  493 = 5️⃣ ✖️ 💯 ➖ 7️⃣
  494 = 5️⃣ ✖️ 💯 ➖ 6️⃣
  495 = 1️⃣ ➕ 5️⃣ ✖️ 💯 ➖ 6️⃣
  496 = 5️⃣ ✖️ 💯 ➖ 4️⃣
  497 = 5️⃣ ✖️ 💯 ➖ 3️⃣
  498 = 5️⃣ ✖️ 💯 ➖ 2️⃣
  499 = 5️⃣ ✖️ 💯 ➖ 1️⃣
  500 = 5️⃣ ✖️ 💯
  501 = 1️⃣ ➕ 5️⃣ ✖️ 💯
  502 = 2️⃣ ➕ 5️⃣ ✖️ 💯
  503 = 3️⃣ ➕ 5️⃣ ✖️ 💯
  504 = 4️⃣ ➕ 5️⃣ ✖️ 💯
  505 = 5️⃣ ➕ 🔟 ✖️ 💯 ➗ 2️⃣
  506 = 5️⃣ ✖️ 💯 ➕ 6️⃣
  507 = 5️⃣ ✖️ 💯 ➕ 7️⃣
  508 = 5️⃣ ✖️ 💯 ➕ 8️⃣
  509 = 5️⃣ ✖️ 💯 ➕ 9️⃣
  510 = 5️⃣ ✖️ 💯 ➕ 🔟
  ...
  590 = 6️⃣ ✖️ 💯 ➖ 🔟
  591 = 6️⃣ ✖️ 💯 ➖ 9️⃣
  592 = 6️⃣ ✖️ 💯 ➖ 8️⃣
  593 = 6️⃣ ✖️ 💯 ➖ 7️⃣
  594 = 1️⃣ ➕ 6️⃣ ✖️ 💯 ➖ 7️⃣
  595 = 6️⃣ ✖️ 💯 ➖ 5️⃣
  596 = 6️⃣ ✖️ 💯 ➖ 4️⃣
  597 = 6️⃣ ✖️ 💯 ➖ 3️⃣
  598 = 6️⃣ ✖️ 💯 ➖ 2️⃣
  599 = 6️⃣ ✖️ 💯 ➖ 1️⃣
  600 = 6️⃣ ✖️ 💯
  601 = 1️⃣ ➕ 6️⃣ ✖️ 💯
  602 = 2️⃣ ➕ 6️⃣ ✖️ 💯
  603 = 3️⃣ ➕ 6️⃣ ✖️ 💯
  604 = 4️⃣ ➕ 6️⃣ ✖️ 💯
  605 = 5️⃣ ➕ 6️⃣ ✖️ 💯
  606 = 6️⃣ ✖️ 💯 ➕ 7️⃣ ➖ 1️⃣
  607 = 6️⃣ ✖️ 💯 ➕ 7️⃣
  608 = 6️⃣ ✖️ 💯 ➕ 8️⃣
  609 = 6️⃣ ✖️ 💯 ➕ 9️⃣
  610 = 6️⃣ ✖️ 💯 ➕ 🔟
  ...
  690 = 7️⃣ ✖️ 💯 ➖ 🔟
  691 = 7️⃣ ✖️ 💯 ➖ 9️⃣
  692 = 7️⃣ ✖️ 💯 ➖ 8️⃣
  693 = 1️⃣ ➕ 7️⃣ ✖️ 💯 ➖ 8️⃣
  694 = 7️⃣ ✖️ 💯 ➖ 6️⃣
  695 = 7️⃣ ✖️ 💯 ➖ 5️⃣
  696 = 7️⃣ ✖️ 💯 ➖ 4️⃣
  697 = 7️⃣ ✖️ 💯 ➖ 3️⃣
  698 = 7️⃣ ✖️ 💯 ➖ 2️⃣
  699 = 7️⃣ ✖️ 💯 ➖ 1️⃣
  700 = 7️⃣ ✖️ 💯
  701 = 1️⃣ ➕ 7️⃣ ✖️ 💯
  702 = 2️⃣ ➕ 7️⃣ ✖️ 💯
  703 = 3️⃣ ➕ 7️⃣ ✖️ 💯
  704 = 4️⃣ ➕ 7️⃣ ✖️ 💯
  705 = 5️⃣ ➕ 7️⃣ ✖️ 💯
  706 = 6️⃣ ➕ 7️⃣ ✖️ 💯
  707 = 7️⃣ ✖️ 💯 ➕ 8️⃣ ➖ 1️⃣
  708 = 7️⃣ ✖️ 💯 ➕ 8️⃣
  709 = 7️⃣ ✖️ 💯 ➕ 9️⃣
  710 = 7️⃣ ✖️ 💯 ➕ 🔟
  ...
  790 = 8️⃣ ✖️ 💯 ➖ 🔟
  791 = 8️⃣ ✖️ 💯 ➖ 9️⃣
  792 = 1️⃣ ➕ 8️⃣ ✖️ 💯 ➖ 9️⃣
  793 = 8️⃣ ✖️ 💯 ➖ 7️⃣
  794 = 8️⃣ ✖️ 💯 ➖ 6️⃣
  795 = 8️⃣ ✖️ 💯 ➖ 5️⃣
  796 = 8️⃣ ✖️ 💯 ➖ 4️⃣
  797 = 8️⃣ ✖️ 💯 ➖ 3️⃣
  798 = 8️⃣ ✖️ 💯 ➖ 2️⃣
  799 = 8️⃣ ✖️ 💯 ➖ 1️⃣
  800 = 8️⃣ ✖️ 💯
  801 = 1️⃣ ➕ 8️⃣ ✖️ 💯
  802 = 2️⃣ ➕ 8️⃣ ✖️ 💯
  803 = 3️⃣ ➕ 8️⃣ ✖️ 💯
  804 = 4️⃣ ➕ 8️⃣ ✖️ 💯
  805 = 5️⃣ ➕ 8️⃣ ✖️ 💯
  806 = 6️⃣ ➕ 8️⃣ ✖️ 💯
  807 = 7️⃣ ➕ 8️⃣ ✖️ 💯
  808 = 8️⃣ ✖️ 💯 ➕ 9️⃣ ➖ 1️⃣
  809 = 8️⃣ ✖️ 💯 ➕ 9️⃣
  810 = 8️⃣ ✖️ 💯 ➕ 🔟
  ...
  890 = 9️⃣ ✖️ 💯 ➖ 🔟
  891 = 1️⃣ ➕ 9️⃣ ✖️ 💯 ➖ 🔟
  892 = 9️⃣ ✖️ 💯 ➖ 8️⃣
  893 = 9️⃣ ✖️ 💯 ➖ 7️⃣
  894 = 9️⃣ ✖️ 💯 ➖ 6️⃣
  895 = 9️⃣ ✖️ 💯 ➖ 5️⃣
  896 = 9️⃣ ✖️ 💯 ➖ 4️⃣
  897 = 9️⃣ ✖️ 💯 ➖ 3️⃣
  898 = 9️⃣ ✖️ 💯 ➖ 2️⃣
  899 = 9️⃣ ✖️ 💯 ➖ 1️⃣
  900 = 9️⃣ ✖️ 💯
  901 = 1️⃣ ➕ 9️⃣ ✖️ 💯
  902 = 2️⃣ ➕ 9️⃣ ✖️ 💯
  903 = 3️⃣ ➕ 9️⃣ ✖️ 💯
  904 = 4️⃣ ➕ 9️⃣ ✖️ 💯
  905 = 5️⃣ ➕ 9️⃣ ✖️ 💯
  906 = 6️⃣ ➕ 9️⃣ ✖️ 💯
  907 = 7️⃣ ➕ 9️⃣ ✖️ 💯
  908 = 8️⃣ ➕ 9️⃣ ✖️ 💯
  909 = 9️⃣ ✖️ 💯 ➕ 🔟 ➖ 1️⃣
  910 = 9️⃣ ✖️ 💯 ➕ 🔟
  ...
  991 = 🔟 ✖️ 💯 ➖ 9️⃣
  992 = 🔟 ✖️ 💯 ➖ 8️⃣
  993 = 🔟 ✖️ 💯 ➖ 7️⃣
  994 = 🔟 ✖️ 💯 ➖ 6️⃣
  995 = 🔟 ✖️ 💯 ➖ 5️⃣
  996 = 🔟 ✖️ 💯 ➖ 4️⃣
  997 = 🔟 ✖️ 💯 ➖ 3️⃣
  998 = 🔟 ✖️ 💯 ➖ 2️⃣
  999 = 🔟 ✖️ 💯 ➖ 1️⃣
 1000 = 🔟 ✖️ 💯
 1001 = 1️⃣ ➕ 🔟 ✖️ 💯
 1002 = 2️⃣ ➕ 🔟 ✖️ 💯
 1003 = 3️⃣ ➕ 🔟 ✖️ 💯
 1004 = 4️⃣ ➕ 🔟 ✖️ 💯
 1005 = 5️⃣ ➕ 🔟 ✖️ 💯
 1006 = 6️⃣ ➕ 🔟 ✖️ 💯
 1007 = 7️⃣ ➕ 🔟 ✖️ 💯
 1008 = 8️⃣ ➕ 🔟 ✖️ 💯
 1009 = 9️⃣ ➕ 🔟 ✖️ 💯
| improve this answer | |
$\endgroup$
  • $\begingroup$ Great! ➕1️⃣ for directly answering each question. $\endgroup$ – sjwarner Feb 16 at 10:34
  • $\begingroup$ Isn't 1010 1 + 9 + 10 x 100? $\endgroup$ – zixuan Apr 21 at 18:22
  • $\begingroup$ @zixuan You can only use each emoji once. $\endgroup$ – Mark Hobson Apr 22 at 19:14
10
$\begingroup$

Here are my answers for the numbers

-200 through +210.

I believe I have exhaustively enumerated all possible sequences; a proof that the preceding and following numbers are not constructable will be forthcoming.

-200=0-2*100
-199=1-2*100
-198=2-6*100/3
-197=3-2*100
-196=4-2*100
-195=5-2*100
-194=6-2*100
-193=7-2*100
-192=8-2*100
-191=9-2*100
-190=10-2*100
-189=1+10-2*100
-188=3+9-2*100
-187=3+10-2*100
-186=4+10-2*100
-185=5+10-2*100
-184=6+10-2*100
-183=7+10-2*100
-182=8+10-2*100
-181=9+10-2*100
-180=0-9*100/5
-179=1-9*100/5
-178=2-9*100/5
-177=3-9*100/5
-176=4-9*100/5
-175=0-7*100/4
-174=1-7*100/4
-173=2-7*100/4
-172=3-7*100/4
-171=1+3-7*100/4
-170=5-7*100/4
-169=6-7*100/4
-168=1+6-7*100/4
-167=8-7*100/4
-166=9-7*100/4
-165=10-7*100/4
-164=1+10-7*100/4
-163=2+10-7*100/4
-162=3+10-7*100/4
-161=5+9-7*100/4
-160=0-8*100/5
-159=1-8*100/5
-158=2-8*100/5
-157=3-8*100/5
-156=4-8*100/5
-155=1+4-8*100/5
-154=6-8*100/5
-153=7-8*100/5
-152=1+7-8*100/5
-151=9-8*100/5
-150=0-3*100/2
-149=1-3*100/2
-148=2-6*100/4
-147=3-6*100/4
-146=4-3*100/2
-145=5-3*100/2
-144=6-3*100/2
-143=7-3*100/2
-142=8-3*100/2
-141=9-3*100/2
-140=0-7*100/5
-139=1-7*100/5
-138=2-7*100/5
-137=3-7*100/5
-136=4-7*100/5
-135=1+4-7*100/5
-134=6-7*100/5
-133=1+6-7*100/5
-132=8-7*100/5
-131=9-7*100/5
-130=10-7*100/5
-129=1+10-7*100/5
-128=2+10-7*100/5
-127=3+10-7*100/5
-126=4+10-7*100/5
-125=0-5*100/4
-124=1-5*100/4
-123=2-5*100/4
-122=3-5*100/4
-121=4-10*100/8
-120=0-6*100/5
-119=1-6*100/5
-118=2-6*100/5
-117=3-6*100/5
-116=4-6*100/5
-115=10-5*100/4
-114=1+10-5*100/4
-113=7-6*100/5
-112=8-6*100/5
-111=9-6*100/5
-110=10-6*100/5
-109=1+10-6*100/5
-108=2+10-6*100/5
-107=3+10-6*100/5
-106=4+10-6*100/5
-105=7+8-6*100/5
-104=7+9-6*100/5
-103=7+10-6*100/5
-102=8+10-6*100/5
-101=9+10-6*100/5
-100=0-100
-99=1-100
-98=2-100
-97=3-100
-96=4-100
-95=5-100
-94=6-100
-93=7-100
-92=8-100
-91=9-100
-90=10-100
-89=1+10-100
-88=2+10-100
-87=3+10-100
-86=4+10-100
-85=5+10-100
-84=6+10-100
-83=7+10-100
-82=8+10-100
-81=9+10-100
-80=0-8*10
-79=1-8*10
-78=2-8*10
-77=3-8*10
-76=4-8*10
-75=5-8*10
-74=6-8*10
-73=7-8*10
-72=0-8*9
-71=1-8*9
-70=0-7*10
-69=1-7*10
-68=2-7*10
-67=3-7*10
-66=4-7*10
-65=5-7*10
-64=6-7*10
-63=0-7*9
-62=1-7*9
-61=2-7*9
-60=0-6*10
-59=1-6*10
-58=2-6*10
-57=3-6*10
-56=0-7*8
-55=1-7*8
-54=0-6*9
-53=1-6*9
-52=2-6*9
-51=3-6*9
-50=0-5*10
-49=1-5*10
-48=0-6*8
-47=1-6*8
-46=2-6*8
-45=0-5*9
-44=1-5*9
-43=2-5*9
-42=0-6*7
-41=1-6*7
-40=0-4*10
-39=1-4*10
-38=2-4*10
-37=3-4*10
-36=0-4*9
-35=0-5*7
-34=1-5*7
-33=2-5*7
-32=0-4*8
-31=1-4*8
-30=0-3*10
-29=1-3*10
-28=0-4*7
-27=0-3*9
-26=1-3*9
-25=2-3*9
-24=0-3*8
-23=1-3*8
-22=2-3*8
-21=0-3*7
-20=0-2*10
-19=1-2*10
-18=0-2*9
-17=1-2*9
-16=0-2*8
-15=0-3*5
-14=0-2*7
-13=1-2*7
-12=0-2*6
-11=1-2*6
-10=0-10
-9=0-9
-8=0-8
-7=0-7
-6=0-6
-5=0-5
-4=0-4
-3=0-3
-2=0-2
-1=0-1
0=0
1=1
2=2
3=3
4=4
5=5
6=6
7=7
8=8
9=9
10=10
11=1+10
12=2+10
13=3+10
14=4+10
15=5+10
16=6+10
17=7+10
18=8+10
19=9+10
20=2*10
21=3*7
22=1+3*7
23=2+3*7
24=3*8
25=100/4
26=2+3*8
27=3*9
28=4*7
29=1+4*7
30=3*10
31=1+3*10
32=4*8
33=1+4*8
34=2+4*8
35=5*7
36=4*9
37=1+4*9
38=2+4*9
39=3+4*9
40=4*10
41=1+4*10
42=6*7
43=1+6*7
44=2+6*7
45=5*9
46=1+5*9
47=2+5*9
48=6*8
49=1+6*8
50=5*10
51=1+5*10
52=2+5*10
53=3+5*10
54=6*9
55=1+6*9
56=7*8
57=1+7*8
58=2+7*8
59=3+7*8
60=6*10
61=1+6*10
62=2+6*10
63=7*9
64=1+7*9
65=2+7*9
66=3+7*9
67=4+7*9
68=5+7*9
69=6+7*9
70=7*10
71=1+7*10
72=8*9
73=1+8*9
74=2+8*9
75=3+8*9
76=4+8*9
77=5+8*9
78=6+8*9
79=7+8*9
80=8*10
81=1+8*10
82=2+8*10
83=3+8*10
84=4+8*10
85=5+8*10
86=6+8*10
87=7+8*10
88=100-2*6
89=9+8*10
90=100-10
91=100-9
92=100-8
93=100-7
94=100-6
95=100-5
96=100-4
97=100-3
98=100-2
99=100-1
100=100
101=1+100
102=2+100
103=3+100
104=4+100
105=5+100
106=6+100
107=7+100
108=8+100
109=9+100
110=10+100
111=100+2*6-1
112=100+2*6
113=100+2*7-1
114=100+2*7
115=100+3*5
116=100+2*8
117=100+2*9-1
118=100+2*9
119=100+2*10-1
120=100+2*10
121=100+3*7
122=100+3*8-2
123=100+3*8-1
124=100+3*8
125=5*100/4
126=100+3*9-1
127=100+3*9
128=100+4*7
129=100+3*10-1
130=100+3*10
131=100+4*8-1
132=100+4*8
133=100+5*7-2
134=100+5*7-1
135=100+5*7
136=100+4*9
137=100+4*10-3
138=100+4*10-2
139=100+4*10-1
140=100+4*10
141=100+6*7-1
142=100+6*7
143=100+5*9-2
144=100+5*9-1
145=100+5*9
146=100+6*8-2
147=100+6*8-1
148=100+6*8
149=100+5*10-1
150=100+5*10
151=100+6*9-3
152=100+6*9-2
153=100+6*9-1
154=100+6*9
155=100+7*8-1
156=100+7*8
157=100+6*10-3
158=100+6*10-2
159=100+6*10-1
160=100+6*10
161=100+7*9-2
162=100+7*9-1
163=100+7*9
164=100+7*10-6
165=100+7*10-5
166=100+7*10-4
167=100+7*10-3
168=100+7*10-2
169=100+7*10-1
170=100+7*10
171=100+8*9-1
172=100+8*9
173=100+8*10-7
174=100+8*10-6
175=7*100/4
176=100+8*10-4
177=100+8*10-3
178=100+8*10-2
179=100+8*10-1
180=100+8*10
181=1+9*100/5
182=100+9*10-8
183=100+9*10-7
184=100+9*10-6
185=100+9*10-5
186=100+9*10-4
187=100+9*10-3
188=100+9*10-2
189=100+9*10-1
190=100+9*10
191=2*100-9
192=2*100-8
193=2*100-7
194=2*100-6
195=2*100-5
196=2*100-4
197=2*100-3
198=1+2*100-3
199=2*100-1
200=2*100
201=1+2*100
202=3+2*100-1
203=3+2*100
204=4+2*100
205=5+2*100
206=6+2*100
207=7+2*100
208=8+2*100
209=9+2*100
210=10+2*100

| improve this answer | |
$\endgroup$
  • 1
    $\begingroup$ where are -196 to -191? $\endgroup$ – athin Feb 12 at 7:13
  • 1
    $\begingroup$ @athin : Everything from -200 to -190 can be done by the same method (except for -198, which has to be an exception to avoid repeating 2). So they should be included to make this list complete, but at least we know that they can be done. $\endgroup$ – Toby Bartels Feb 12 at 9:09
  • $\begingroup$ what about 211..217? 20+2*100-9 ... 20+2*100-3 $\endgroup$ – AKroell Feb 12 at 12:29
  • $\begingroup$ Hi @AKroell - where has each of the 20 come from in those? $\endgroup$ – sjwarner Feb 12 at 14:06
  • 1
    $\begingroup$ Riiight @sjwarner... won't work :D $\endgroup$ – AKroell Feb 12 at 14:25
4
$\begingroup$

-201 cannot be represented like requested. Since 201= 3*67, 67 prime, it cannot be obtained by only multiplication/division. The smallest positive number larger than 201 that can be obtained by one multiplication and division is 225 = 9*100/4. Using the scheme

 a - 9*100/4 + b
 
we can add two positive numbers to -225. The largest remaining ones are 10,8, so
 -207 = 8- 9*100/4 + 10
 
is representable. But all numbers from -201 .. -206 are not.

Similar reasoning applies to 211: it is a prime. It is equal to 200 +11, but 11 cannot be written as quotient or difference (sum/product already used). It is equal to 225-15, but -15 cannot be written with one subtraction without multiplication. So 211 is not reachable, as are 211..214. The next reachable one is

 215 = 9 * 100 / 4 -10
 

| improve this answer | |
$\endgroup$
  • $\begingroup$ Nice reasoning there @daw! $\endgroup$ – sjwarner Feb 12 at 14:07
3
$\begingroup$

Partial answer -- Feel free to use this for your own answer.

I believe the solution for the first question is:

181

Below I have a list of equations for positive integers up to that value. I've omitted over some of the values when the pattern can be surmised.

0 = 0
1 = 1
2 = 2
[...]
10 = 10
11 = 10 + 1
[...]
19 = 10 + 9
20 = 2 * 10
21 = 2 * 10 + 1
22 = 3 * 10 - 8
23 = 2 * 10 + 3
[...]
29 = 2 * 10 + 9
30 = 3 * 10
31 = 3 * 10 + 1
32 = 3 * 10 + 2
33 = 4 * 10 - 7
34 = 3 * 10 + 4
[...]
39 = 3 * 10 + 9
40 = 4 * 10
41 = 4 * 10 + 1
[...]
43 = 4 * 10 + 3
44 = 5 * 10 - 6
[...]
49 = 4 * 10 + 9
50 = 5 * 10
51 = 5 * 10 + 1
[...]
54 = 5 * 10 + 4
55 = 5 * 9 + 10
56 = 5 * 10 + 6
[...]
60 = 6 * 10
[...]
66 = 7 * 10 - 4
[...]
69 = 6 * 10 + 9
70 = 7 * 10
[...]
77 = 8 * 10 - 3
[...]
79 = 7 * 10 + 9
80 = 8 * 10
[...]
88 = 9 * 10 - 2
[...]
89 = 8 * 10 + 9
90 = 9 * 10
91 = 100 - 9
[...]
99 = 100 - 1
100 = 100
101 = 100 + 1
[...]
110 = 100 + 10
111 = 100 + 10 * 2 - 9
112 = 100 + 10 * 2 - 8
[...]
117 = 100 + 10 * 2 - 3
118 = 100 + 9 * 2
119 = 100 + 10 * 2 - 1
120 = 100 + 10 * 2
121 = 100 + 10 * 3 - 9
[...]
127 = 100 + 9 * 3
129 = 100 + 10 * 3 - 1
130 = 100 + 10 * 3
131 = 100 + 10 * 4 - 9
[...]
136 = 100 + 9 * 4
[...]
139 = 100 + 10 * 4 - 1
140 = 100 + 10 * 4
141 = 100 + 10 * 5
[...]
145 = 100 + 9 * 5
[...]
149 = 100 + 10 * 5 - 1
150 = 100 + 10 * 5
151 = 100 + 10 * 6 - 9
[...]
154 = 100 + 9 * 6
[...]
159 = 100 + 10 * 6 - 1
160 = 100 + 10 * 6
161 = 100 + 10 * 7 - 9
[...]
163 = 100 + 9 * 7
[...]
169 = 100 + 10 * 7 - 1
170 = 100 + 10 * 7
171 = 100 + 10 * 8 - 9
[...]
172 = 100 + 9 * 8
[...]
179 = 100 + 10 * 8 - 1
180 = 100 + 10 * 8 
181 = 100 + 10 * 9 (no way to subtract 9)
181 = 100 * 2 (no way to subtract 19)
181 = 100 + 10 * 8 (no way to add 1 since the + is already used)
| improve this answer | |
$\endgroup$
  • $\begingroup$ Hey @Tonkleton! Nice start - I like the repetition in groups, makes the process easier to follow. I've found 181 and some numbers above are possible, but not using this pattern! $\endgroup$ – sjwarner Feb 11 at 21:20
  • $\begingroup$ Very nice, looking forward to seeing your solution! Feel free to use any part of mine that you like. :) $\endgroup$ – Tonkleton Feb 11 at 21:27
  • $\begingroup$ 181 to 190 can be done - just use 100 + the existing formulas for 81 to 90. Have to think about 191. $\endgroup$ – Eugene Styer Feb 11 at 21:54
  • 1
    $\begingroup$ @EugeneStyer If we reused to formula for 81, we'd have 100 + 8 * 10 + 1 which has two +'s. I don't think we can use the + operator twice since the + emojis would stack up. $\endgroup$ – Tonkleton Feb 11 at 22:20
  • 1
    $\begingroup$ Well, we have 181 in another answer now, as 1+9*100/5. $\endgroup$ – Toby Bartels Feb 12 at 9:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.