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Four Triangles Puzzle

5 to 11

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Algebra from Geometry
problem

Algebra From Geometry

11 to 16
Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.
Number Spirals
problem

Number Spirals

7 to 11
This task opens up an investigation of a different kind of spiral. This may open doors to new ideas.
Binomial
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Binomial

16 to 18

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

Arithmagons
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Arithmagons

11 to 16

Can you find the values at the vertices when you know the values on the edges?

Tables Without Tens
problem

Tables Without Tens

7 to 11

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Endorsement
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Endorsement

Find out where NRICH has been recommended.

Score
problem

Score

11 to 14
There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers?
Cushion Ball
problem

Cushion Ball

16 to 18
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
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