### 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?

# Square Ratio

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

A square is divided into four congruent rectangles and a smaller square, as shown.
(The diagram is not to scale.)

The area of the small square is 1/4 of the area of the whole square.

What is the ratio of the length of a short side of one of the rectangles to the length of a long side?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.