1 out of 3
2 out of 3
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.
2 out of 3
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.
3 out of 3
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
3 out of 3
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.
3 out of 3
Weekly Problem 6 - 2010
Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?
1 out of 3
This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
2 out of 3
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
3 out of 3
How many divisors does factorial n (n!) have?
3 out of 3
Show that it is rare for a ratio of ratios to be rational.
