Are all of the numbers in a certain list of 15 numbers equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.
My explanation is similar to Entwistle's explanation.
Here's my explanation.
(1)- Trivial Case: All numbers in the list are 4.
Alternative Case: All but two numbers in the list are 4; the others are 3 and 5. Please that this alternative case is only one of many alternative cases; for example, all but 3 numbers could be 4, and the remaining three numbers could be 3,4, and 5.
(2) implies that for numbers a,b,c,d,e,f,g,h,i,j,k,l,m,n,o, in the the list of 15 numbers,
To cover a and b, note: c+d+e=b+d+e-->b=c
Thus all numbers in the list are equal.