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.
- 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:
- What is the smallest positive integer that I will not be able to make an equation for?
- What is the largest negative integer that I will not be able to make an equation for?
- 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'.