Tuesday puzzle

Re: Tuesday puzzle

Bill Earl

The square, triangular one that's not one.

Close, but no 

I was 3/4 right....

Bill Earl

This time I let the computer do the work.

Re: Tuesday puzzle

Don Orr

36?

A popular answer, but no 

Solution

Alex Y

Kudos to Bill for this one.

48 has 10 divisors: 1,2,3,4,6,8,12,16,24,and 48.

36 was close, with 9 divisors: 1,2,3,4,6,9,12,18, and 36.

An interesting observation here: If the prime factorization of a number is

p1^n1 * p2^n2 * ... *pk^nk, then the number of divisors is (n1+1) * (n2+1) * ... * (nk+1). Why? Every divisor has to be the product of the same factors, just to different powers. Each prime factor can appear in a divisor from zero to n times. The count of possible divisors is the number of combinations of those prime factors, given by the product of the numbers of times the prime factors can appear.

36 = 2^2 * 3^2, and (2+1)*(2+1) = 9

48 = 2*4 * 3^1, and (4+1)*(1+1) = 10