Problems
Worms
Stage:2 Challenge Level:
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Little Boxes
Stage:2 Challenge Level:
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Legs Eleven
Stage:3 Challenge Level:
Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?
More Marbles
Stage:3 Challenge Level:
I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?
Find the Fake
Stage:4 Challenge Level:
There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. What is the minimum number of weighings needed to locate the fake coin?
Roaming Rhombus
Stage:4 Challenge Level:
We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .
Ordered Sums
Stage:4 Challenge Level:
Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .
Ball Packing
Stage:4 Challenge Level:
If a ball is rolled into the corner of a room how far is its centre from the corner?
Origami
Stage:4 Challenge Level:
Take a sheet of A4 paper and place it in landscape format. Fold up the bottom left corner to the top so the double thickness is a 45,45,90 triangle. Fold up the bottom right corner to meet. . . .
Hexy-metry
Stage:4 and 5 Challenge Level:
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Three by One
Stage:5 Challenge Level:
NRICH has always had good solutions from Madras College in St Andrew's, Scotland but the solutions to this problem were truly exceptional.
