Here is a link to the problem I'm talking about. Does anybody know how to solve this? https://www.newyearofpuzzles.com/teaser
Decided to post on CF because there are lots of smart people here. This is my idea right now:
Solution idea
The hint says you don't need a calculator but the only solution I can come up with would need a calculator. Unless there is some way to do these combinatorics in your head.
have you tried FFT?
We have initial power of 4, and intended final power of 12,848. So, the net increase in power needs to be
12848 - 4 = 12844
.Since power 4 is 1st shot and 12,848 is the 100,000th shot, we have 99,999 moves to increase the power by a net difference of 12844. Since we can change power by only exactly 2 in each move, out of the 99,999 moves, we will have
12844/2 = 6422
extra +2 power moves than -2 moves. You have solved till this point.That means
99,999 - 6422 = some_odd_number
. Now, thissome_odd_number
must be evenly divided into +2 and -2 (so that they cancel out), but it is impossible, since it is an odd number. So the answer is 0.