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Repeaters
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Helen's Conjecture
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Age 11 to 14 Short Challenge Level:
In 2016, the 29$^{\text{th}}$ of February was a Monday. When will be the next leap year when the 29$^{\text{th}}$ of February is a Monday?
This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.