### 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

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

### Fibs

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

# Knockdown

##### Age 11 to 14 Short Challenge Level:

Pegs numbered $1$ to $50$ are placed in order in a line, with number $1$ on the left.

They are then knocked over, one at a time, following these rules:
• Starting with the first standing peg on the left, alternate pegs are knocked down, until the end of the row is reached.
• Each time the end of the row is reached, repeat the previous rule.
What is the number of the last peg to be knocked down?

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

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.