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An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?
Age
11 to 14
Challenge level
Problem
An examination paper is made by taking 5 large sheets of paper, folding the pile in half and stapling it. The pages are then numbered in order from 1 to 20. What is the sum of the three page numbers that are on the same sheet of paper as page number 5?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
The first large sheet of paper will hold pages 1, 2, 19 and 20; the second will hold pages 3, 4, 17 and 18; the third will hold pages 5, 6, 15 and 16.
Hence, the required sum is 37.
Alternatively, one could note that the sum of all four page numbers on one large sheet of paper is always 42. So the required sum is 42 - 5 = 37.