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

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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?

Suit Sequence

Age 11 to 14 Short Challenge Level:

A pattern that repeats every six symbols starts as shown below:  $$ \heartsuit \:\: \clubsuit \:\: \heartsuit \:\: \diamondsuit \:\: \heartsuit \:\: \spadesuit \:\: \heartsuit \:\: \clubsuit \:\: \heartsuit \:\: \diamondsuit \:\: \heartsuit \:\: \spadesuit \:\: \ldots$$ What are the $100^{\text{th}}$ and $101^{\text{st}}$ symbols in the pattern?


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.