get 100 with the help of five 2

Question

how to get 100 with the help of +, -, /, * and five 2s?

22222 = 100

I should put arithmetic operants between two s and get 100. PLease help

Answer 1

This seems to be impossible without a sixth 2 or the power operation. (If either were allowed, you could use (222-22)/2 or ((22-2)/2)^2.) I assumed parentheses are allowed although they were not explicitly mentioned. Disallowing them doesn't help reaching 100.

First, you have to group the twos into numbers. Five twos (2,2,2,2,2) can't give more than 32, so it's not enough. If you have a 222, the possible combinations are (222,2,2) and (222,22) and it's relatively easy to check that these don't give 100. It's even easier to see that (2222,2) and (22222) don't work.

The grouping (22,22,2) doesn't work either. If you first take a binary operation between 22 and 22, you are too far from 100. If you first modify one of the 22s by the 2, you get 24, 20, 11 or 44, and none of these numbers together with 22 can give 100.

The only thing left is (22,2,2,2). The three 2s can't make anything larger than 8 together, so in order to get anywhere near 100 you have to multiply the 22 with something (possibly after adding or subtracting something). Multiplying 22 directly doesn't work: the first reasonably large multiple is 22*2*2=88 and you can't correct this into 100 with a single 2.

So we have to add or subtract something before multiplying. But then we can only use two 2s for the multiplier (which has to be at least four to make the result big enough). This leaves (22+2)*2*2=96 and (22-2)*2*2=80, neither of which is 100.

Notes: My grouping notation does not imply any particular order. When carrying out the operations, it seems most convenient to start with the biggest number (like 22 or 222) and operating on it with other numbers (or their allowed combinations); this doesn't leave anything out. It is of course possible that I have made a mistake somewhere – do let me know if there is something fishy left.

Answer 2

Two possible conclusions: 1) The question is ill-posed (what is the EXACT formulation of the question by the way?) 2) Play dumb: 2-22/22 = 1+0+0