Question

Find all sets of four consecutive integers whose sum is between 95 and 105

Answer 1

Hello,
Let n-2,n-1,n,n+1 the four consecutive integers.

s=n-2+n-1+n+n+1=4n-2
==> 95<=4n-2<=105
==> 97<=4n<=107
==>24.25<=n<=26.75

n= 25 ou n=26
if n=25, s=23+24+25+26=98
if n=26, s=24+25+26+27=102

2 solutions: {23,24,25,26} and {24,25,26,27}