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Numbers in Rows

These problems are a precursor to magic T-hexagons, as the numbers used are repeated, and not all the triangles have to have numbers in them. However, these simplifications made the problems approachable by the competition teams and did draw on ideas that the teams had worked on earlier ... the transversal questions.

Problem 1

Write the numbers 1 - 5 on counters as shown below:

Find a way to position the counters in the triangles that make up a T-hexagon of side 2 such that the total of the numbers in each row of triangles is the same.

Note: Not every triangle has to have a number in it as there are not enough counters to go round. But every row has to have the same total.

Problem 2

You have a set of counters numbered as follows:

Can you find a way to position the counters in the triangles that make up the hexagon such that the total of the numbers in each row of triangles is the same?

Put another way – can you make a magic hexagon with four sets of the numbers 1 – 6?

Problem 3

You have a set of counters numbered as in Problem 2, but this time, try to make the inner hexagon have the same total as each of the sides.

As you do this, you will notice that the total of the numbers in the white triangles on the left and those on the right have to add to the same total. What different totals can these be, and how should the four sets of numbers 1 - 6 be positioned to make the inner hexagon add to the same as the sides.