mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths LIV

Archive

Show me a Random Puzzle
▼ show ▼
Posted on 2016-07-17

Cross Diagonal Cover Problem

Draw with an $$m\times n$$ rectangle, split into unit squares. Starting in the top left corner, move at 45° across the rectangle. When you reach the side, bounce off. Continue until you reach another corner of the rectangle:
How many squares will be coloured in when the process ends?

Combining Multiples

In each of these questions, positive integers should be taken to include 0.
1. What is the largest number that cannot be written in the form $$3a+5b$$, where $$a$$ and $$b$$ are positive integers?
2. What is the largest number that cannot be written in the form $$3a+7b$$, where $$a$$ and $$b$$ are positive integers?
3. What is the largest number that cannot be written in the form $$10a+11b$$, where $$a$$ and $$b$$ are positive integers?
4. Given $$n$$ and $$m$$, what is the largest number that cannot be written in the form $$na+mb$$, where $$a$$ and $$b$$ are positive integers?

Hat Check

Three logicians, A, B and C, are wearing hats. Each has a strictly positive integer written on it. The number on one of the hats is the sum of the numbers on the other two.
The logicians say:
A: I don't know the number on my hat.
B: The number on my hat is 15.
Which numbers are on hats A and C?

Tags: logic
If you enjoyed this puzzle, check out Sunday Afternoon Maths LXII,
puzzles about chalkdust crossnumber, or a random puzzle.