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#65 Prime magic squares

Set by Peter Rowlett

A magic square is an arrangement of numbers where all rows, columns and diagonals add up to the same number, called the magic constant. Can you complete this square by filling in the missing numbers?

This square was discovered in the early 20th century by Henry Dudeney as a magic square of prime numbers. Unfortunately, it contains 1. Modern mathematicians define prime numbers so that 1 isn鈥檛 prime, because it makes lots of results less awkward to state.

An alternative magic square of prime numbers uses 5, 17, 29, 47, 59, 71, 89, 101 and 113.

What is its magic constant?

Can you form these numbers into a magic square?

Solution next week

#64 Matching tiles

Solution

There are 3 脳 3 脳 3 脳 3 脳 3 tiles, or 243.

Any pair of tiles forms a meld with exactly one other tile. There are 242 choices for the second tile and one for the last. However, this counts each meld twice, so there are 121 possible melds that include a given tile.

Each tile is part of 121 melds, making 121 脳 243 possible melds. However, this counts each meld three times, so there are 121 脳 81 = 9801 possible melds altogether.