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The Mean Problem

Age 11 to 14
ShortChallenge Level Yellow starYellow star
Secondary curriculum
  • Problem
  • Solutions

If the first two numbers have a mean of 4, then they have to add up to 8.

If the first three numbers have a mean of 9, they have to add up to 27.

Therefore the third number has to be 27 $-$ 8 = 19

The sum of the four numbers has to be 15 $\times$ 4 = 60

Therefore the fourth number had to be 60 $-$ 27 = 33

If one of the numbers is 2, and the sum of the first two numbers is eight, the second number must be 6.

So alongside 2, the other three numbers are 6, 19 and 33.

 

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

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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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