6. Lucy has lots of identical lolly sticks. She arranges the lolly sticks end to end to make different triangles. Which number of lolly sticks could she not use to make a triangle?
A 7
B 6
C 5
D 4
E 3
6. D Let us consider each lollystick as having length 1. Hence the number of lollysticks used will be the length of the perimeter of the triangle and the question is then equivalent to asking if triangles with the given perimeters can be drawn with integer length sides. A triangle of perimeter 7 is possible with sides 2,2 and 3 (or 3,3 and 1 ), perimeter 6 is possible with sides 2, 2 and 2, perimeter 5 with sides 2,2 and 1 and perimeter 3 with sides 1,1 and 1 . However, it is impossible to create a triangle with perimeter 4 since the largest possible sum for the lengths of the two shortest sides is $1+1=2$ and this is not greater than the smallest possible length of the largest side. Hence the answer is 4 .