Below is a selection of Questions from past and present Puzzle Sheets.
Current Puzzle Sheets and solutions may be found outside the Maths Office (W14)
April - May 07 Junior Puzzle Sheet
Junior Puzzles April 2007
Solutions to any or all of the puzzles are invited from any boy in year 7, 8 or 9. There will be a small prize for the best entries and quite possibly distinctions! Solutions explaining how the answer was found (that is, don’t just hand in the answers), should be given to Mr Brumby by Friday 25th May
Section A
1. How many different numbers are there between 1 and 1000 inclusive that are not divisible by 2 or 5?
2. How many different numbers are there between 1 and 42875 that are not divisible by 5 or 7?
3. If p and q are two different prime numbers how many different numbers are there between 1 and (pq)3 that are not divisible by p or q?
4. Can you use your answer to 3 to verify your answers to 1 and 2?
Section B
If I could fill my classroom from top to bottom with marbles of radius 1 cm, how many marbles could I fit in the room? If I could then somehow seal my room whilst still being able to pour water into it, how many litres of water could I fit in my room in between the marbles? Ensure that in your answer you tell me what your (sensible) estimate of the size of my room is.
(Note: the formula for the volume of a sphere is 4πr3 ÷ 3 )
May - July 06 Senior Puzzle Sheet
Question 1
Prove that the square of any prime greater than 3 leaves a remainder of 1 when divided by 24
Question 4
n7-n always divides by 42. Can you prove this? It it also my conjecture that this expression must have at least 32 factors for n>2. Show that there are 32 factors for n=2 and find, if possible, the next value of n for which there are 32 factors, or prove that there are no more values of n for which there are 32 factors.
