When they danced as couples there was one person left over.
When they danced in threes one person was left over.
When they danced in fours one person was left over.
When they danced in fives one person was left over.
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What if the problem above was changed?
What if the group sizes were 3,5,7 and 8?
This Starter is a simple problem which can be solved by using the Chinese remainder theorem first published in the 3rd to 5th centuries by the Chinese mathematician Sun Tzu. In its basic form, the Chinese remainder theorem will determine a number n that, when divided by some given divisors, leaves given remainders.
What is the lowest number that
when divided by 3 leaves a remainder of 2,
when divided by 5 leaves a remainder of 3,
and when divided by 7 leaves a remainder of 2?
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The following was one of Alex Bellos' Monday Puzzles published in The Guardian online newspaper. it features the Indian mathematician Brahmagupta during the 7th century AD posed the following problem:
When eggs in a basket are taken out 2, 3, 4, 5 and 6 at a time, there remain 1, 2, 3, 4 and 5 eggs respectively. When they are taken out 7 at a time, none are leftover.
Find the smallest number of eggs that could be in the basket.
Teacher, do your students have access to computers such as tablets, iPads or Laptops? This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:
However it would be better to assign one of the student interactive activities below.
Here is the URL which will take them to a student number patterns activity.
An interactive calculator designed to solve this type of problem is available to teachers, parents and turors when signed in.
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