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...

Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Even So

Stage: 3 Challenge Level:

Find some triples of whole numbers $a$, $b$ and $c$ such that $a^2 + b^2 + c^2$ is a multiple of 4. Is it necessarily the case that $a$, $b$ and $c$ must all be even? If so, can you explain why?