2023 AMC 8 Problems/Problem 21
Animated Video Solution
~Star League (https://starleague.us)
Written Solution
First we need to find the sum of each group when split. This is the total sum of all the elements divided by the # of groups. . Then dividing by we have so each group of must have a sum of 15. To make the counting easier we we will just see the possible groups 9 can be with. The posible groups 9 can be with with 2 distinct numbers are and . Going down each of these avenues we will repeat the same process for using the remaining elements in the list. Where there is only 1 set of elements getting the sum of , needs in both cases. After is decided the remaining 3 elements are forced in a group. Yielding us an answer of as our sets are and
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat