you have a pair of newborn hamsters. each pair that is at least one month old produces a new pair every month. at this rate, you will have 178 hamsters at the end of what month? (The math relay officials said the 10th month but I think that it should be the 8th)

Answer 1

so
2 + 4 + 8 + 16 + ... = 178

sum(n) = a(r^n - 1)/(r-1)
2(2^n - 1)/1 = 178
2^n - 1 = 89
2^n = 90

I know 2^6 = 64
2^7 = 128
2^8 = 256

So I agree with your answer ,
at the end of 7 you only have 128 but you need 178
so it must be the 8th month

how did they come up with 10?
perhaps they interpreted their own question incorrectly and found the term number close to 178
let's see which term number is close to 178

term(n) = ar^(n-1)
2(2^(n-1)) = 178
2^(n-1) = 98
n-1 = ln 98/ln2
= 6.6 not anywhere near 10

so , they must be wrong.