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Square Sum

Age 14 to 16
ShortChallenge Level Yellow starYellow star
Secondary curriculum
  • Problem
  • Solutions

One of the following is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

A. 118
B. 128
C. 138
D. 148
E. 158

If you liked this problem, here is an NRICH task which 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.

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Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Triangular Triples

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

Iff

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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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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