| 1. The number 11...122...25 has 1997 1s and 1998 2s. Show that it is a perfect square. |
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| 2. The convex pentagon ABCDE has AB = AE = CD = 1 and angle ABC = angle DEA = 90o and BC + DE = 1. Find its area. | |
| 3. Find all positive integers m, n such that mn = nm-n. |
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| 4. Do there exist 16 three digit numbers, using only three different digits in all, so that the numbers are all different mod 16? |
To avoid possible copyright problems, I have changed the wording, but not the substance, of the problems.
© John Scholes
jscholes@kalva.demon.co.uk
29 Jul 2003
Last updated/corrected 29 Jul 2003