### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Have You Got It?

Can you explain the strategy for winning this game with any target?

### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

# Birthday Tables

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

Mark has lots of tables in his (large) house. Each circular table will seat $5$ people and each rectangular table will seat $8$ people.

At his birthday party there will be $36$ people, including himself.

Mark wants there to be no empty seats at any of the tables that are used.

How many tables of each type does Mark need to use in order to achieve this?
Is this the only possibility?

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.