Question

A shop assistant was to stack 45 cereal boxes in a display window. The manager wanted all 45 boxes to be used and the boxes to be stacked in a triangle. How many boxes needed to be placed on the bottom row to build the display?

Answer 1

Because the display will be triangular then the number of boxes in the row will increase by an arithmetic progression with a step of 1 from 1 box to n boxes

The formula of sum of an arithmetic progression in increments of 1:

$$\frac{(1+n)n}{2}=45$$

it follows that n=9

Anwser n=9;