# 2019 is coming!

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.

• Are these solutions possible? – QuantumTwinkie Sep 12 '18 at 21:26
• @QuantumTwinkie let's find out! :D – Mr Pie Sep 12 '18 at 21:47
• @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. – rhsquared Sep 13 '18 at 2:36
• @user477343 You are quite right. Maybe I won't be allowed to answer because of the implicit two in my name. – rhsquared Sep 13 '18 at 6:01
• Are bare decimal points allowed, like $.1$ and $.2$? – nickgard Sep 13 '18 at 8:01

66:

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

74:

$9/.12-0!$

76:

$9/.12+0!$

77:

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

• I think the square function cannot be used – Ian Fako Sep 13 '18 at 9:18
• No it can't even I tried using it. – Quark-epoch Sep 13 '18 at 9:38
• And you can't concatenate to make $12$, either, but $(+1)$ in at least $13$ hours for the effort (DVL) :D – Mr Pie Sep 13 '18 at 10:44
• @user477343 you can concatenate 1 and 2. See examples above 20, 92, 2.9 – Ian Fako Sep 13 '18 at 10:52
• @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. – Mr Pie Sep 13 '18 at 10:54

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

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