AN ODD MAGIC SQUARE
In a "Chinese" magic square, the numbers from 1 to 9 are arranged so that each row, column and diagonal has a total of 15.
Arrange the nine odd numbers from 1 to 17 in a square so that each row, column and diagonal has the same total.
1 3 5 7 9 11 13 15 17
With this rather strange dartboard you use four darts instead of three.
Four friends played darts. They each threw four darts and each dart landed on the board.
Anna scored 81, Bill scored 130, Carrie scored 143, David scored 150 and Ella scored 155.
How many of the darts landed on 42?
SOLUTIONS An odd magic square (age 7-12) The "odd" magic square is obtained from the "Chinese" magic square by doubling each number then subtracting 1.
Different darts (age 9-14) Four darts landed on 42. For example, Anna scored 81 with three 13s and 42. Bill scored 130 with two 42s and two 23s.
Carrie scored 143 with three 31s and 50. David scored 150 with two 50s, 37 and 13. Ella scored 155 with two 50s, 42 and 13. Other scores are possible, but the overall number of 42s is unchanged.