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396

Age 14 to 16
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Student Solutions

The four digits 5, 6, 7 and 8 are put at random in the spaces of the number below:

3 _ 1 _ 4 _ 0 _ 9 2

  • Estimate the probability that the answer will be a multiple of 396.
  • Calculate the probability and explain your answer.

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Novemberish

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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