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A game in which players take it in turns to choose a number. Can you block your opponent?
Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?
This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
An introduction to proof by contradiction, a powerful method of mathematical proof.
Can you make lines of Cuisenaire rods that differ by 1?
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
An introduction to coding and decoding messages and the maths behind how to secretly share information.
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
The sum of the cubes of two numbers is 7163. What are these numbers?