On an adventure holiday five children, called A, B, C, D, E, all take part in five competitions, called V, W, X, Y, Z. In each competition marks of 5, 4, 3, 2, 1 are awarded for coming 1 st , 2 nd , 3 rd , 4 th or 5 th There are no ties for places. Child A scores a total of 24 marks, child C scores the same in each of four competitions, child D scores 4 in competition V, and child E scores 5 in W and 3 in X. Surprisingly, their overall positions are in alphabetical order. Show that this information is enough to find all the scores, and that there is only one solution. Give the marks scored by each child in each competition by filling in a copy of this table.
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Junior Mathematical Olympiad 2004 (2004)
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