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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Number Sandwiches

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Hallway Borders

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

A Mean Tetrahedron

Age 11 to 14
Challenge Level

A tetrahedron has 4 vertices, 6 edges and 4 faces. Can you number them 1 to 14 in such a way that the number on each edge is the mean of the two numbers at the vertices joined by that edge and also the mean of the two numbers on the faces it separates?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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