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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...

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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?

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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?

How Many Rectangles?

Age 11 to 14 Short Challenge Level:

By drawing $9$ lines, $5$ horizontal and $4$ vertical, one can form $12$ small rectangles, as shown on the right. What is the greatest possible number of small rectangles that one can form by drawing $15$ lines, either horizontal or vertical?

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.