Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Series Sums

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

More Number Pyramids

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Natural Sum

Stage: 4 Challenge Level:

The picture illustrates the sum $1 + 2 + 3 + 4 = (4 \times5)/2$. Prove the general formula for the sum of the first $n$ natural numbers and the formula for the sum of the cubes of the first n natural numbers. See the problem Picture Story .