Ms Math's kindergarten class has 16 registered students. The classroom has a very large number, N, of play blocks which satisfies the conditions: (a) If 16, 15, 14 students are present in the class, then in each case all the blocks can be distributed in equal numbers to each student, and (b) There are three integers 0 < x < y < z < 14 such that when x, y, or z students are present and the blocks are distributed in equal numbers to each student, there are exactly three blocks left over. Find the sum of the distinct prime divisors of the least possible value of N satisfying the above conditions.

nchang Apr 1, 2020

#2**0 **

Tricky problems always require some logic. I think we can rule out 1, 2, 3, 4, 5, 7, and 8 due to the parameters put forth in the problem.

Impasta Apr 1, 2020

#3**0 **

After that, there aren't many left. Time to use some more logic, I presume, but I'm lazy and won't do it.

Impasta
Apr 1, 2020

#7**0 **

That is true! Technically, if there are 0 blocks, the blocks can be evenly distributed

AnExtremelyLongName
Apr 1, 2020

#8**-1 **

Read the problem: it says there are a very large number.

This sounds like the meme where the guy asks if n is a lot.

Impasta
Apr 1, 2020

#9**0 **

Aw, but 0 can be very large in a world of negative numbers. I guess we live in a positive world then. Why am I having senseless thoughts.

AnExtremelyLongName
Apr 1, 2020