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Factoring a Million

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

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

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Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

Scratch Cards

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

Chances Are

Which of these games would you play to give yourself the best possible chance of winning a prize?

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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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