6
$\begingroup$

Use $2$ $0$ $1 $ and $9$ to make the numbers $66, 74, 76, and$ $77$

RULES

  1. You must use all 4 digits. Only the digits 2, 0, 1, and 9 can be used. You can make multi-digit numbers out of the numbers. Examples: 20, 92, 2.9

  2. The square function may NOT be used. Nor may the cube, raise to a fourth power, or any other function that raises a number to a specific power. You may use the ^ operation if you use a digit, for example, [(9 + 1)^2 - 0!] is acceptable (if you're trying to get 99), because 2, 0, 1, and 9 is used. However, [20 ^ 2 / 9 + 1] can't be used to get 40 because it uses an extra 2.

  3. Sorry, but the integer function may NOT be used. Nor may the round, floor, ceiling, more than 2 factorials in a row, repeating symbol, or truncate functions.

  4. +, -, *, /, (), !, sqrt, ^, and !! may be used for functions.

  5. I picked these because these are the hardest for 2019. From the numbers 1-100, these are the only ones I didn't get.

Again, no brute-force methods. Good luck.

$\endgroup$
  • $\begingroup$ Are these solutions possible? $\endgroup$ – QuantumTwinkie Sep 12 '18 at 21:26
  • 1
    $\begingroup$ @QuantumTwinkie let's find out! :D $\endgroup$ – user477343 Sep 12 '18 at 21:47
  • 1
    $\begingroup$ @Alto Doesn't using sqrt contradict your requirements? It's an explicit square root, i.e. it uses 2, or, even worse, it could be represented as x^1/2 which uses 1 and 2. $\endgroup$ – rhsquared Sep 13 '18 at 2:36
  • 1
    $\begingroup$ @user477343 You are quite right. Maybe I won't be allowed to answer because of the implicit two in my name. $\endgroup$ – rhsquared Sep 13 '18 at 6:01
  • 1
    $\begingroup$ Are bare decimal points allowed, like $.1$ and $.2$? $\endgroup$ – nickgard Sep 13 '18 at 8:01
7
$\begingroup$

66:

$(\sqrt{9})!\times(12-0!)$

74:

$9/.12-0!$

76:

$9/.12+0!$

77:

$((\sqrt{9})!)!\times.1+(0!/.2)$

$\endgroup$
  • $\begingroup$ I think the square function cannot be used $\endgroup$ – Ian Fako Sep 13 '18 at 9:18
  • $\begingroup$ No it can't even I tried using it. $\endgroup$ – Quark-epoch Sep 13 '18 at 9:38
  • $\begingroup$ And you can't concatenate to make $12$, either, but $(+1)$ in at least $13$ hours for the effort (DVL) :D $\endgroup$ – user477343 Sep 13 '18 at 10:44
  • $\begingroup$ @user477343 you can concatenate 1 and 2. See examples above 20, 92, 2.9 $\endgroup$ – Ian Fako Sep 13 '18 at 10:52
  • $\begingroup$ @IanFako Wait... I thought it said "can't" .... dammit, I would have had more of a chance finding a solution otherwise. Eh well, everything happens for a reason... at least in my philosophy. $\endgroup$ – user477343 Sep 13 '18 at 10:54
0
$\begingroup$

Also here is another solution to 77 that might be easier- (√9!)!*.1+(0!/.2)

The equation doesn't require the use of a double factorial.

KG

$\endgroup$
  • $\begingroup$ You should check the other answers before adding a new one. This is the same as the accepted answer for 77. $\endgroup$ – Herb Wolfe Jan 7 at 21:52

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.