Miscellaneous Combinatorial Puzzles 173- FOOTBALL RESULTS
Near the close of a football season a correspondent informed me that when
he was returning from Glasgow after the international match between Scot-
land and England the following table caught his eye in a newspaper:Goals
Played Won Lost Drawn For Against Points
Scotland 3 3 0 0 7 I 6
England 3 2 3 3
Wales 3 I I 3 3 3
Ireland 3 0 3 0 6 0As he knew, of course, that Scotland had beaten England by 3--0, it struck
him that it might be possible to find the scores in the other five matches from
the table. In this he succeeded. Can you discover from it how many goals
were won, drawn, or lost by each side in every match?
- THE DAMAGED MEASURE
Here is a new puzzle that is interesting, and it reminds one, though it
is really very different, of the classical problem by Bachet concerning the
weight that was broken in pieces which would then allow of any weight
in pounds being determined from one pound up to the total weight of all the
pieces. In the present case a man has a yardstick from which 3 inches have
been broken off, so that it is only 33 inches in length. Some of the graduation
marks are also obliterated, so that only eight of these marks are legible; yet
he is able to measure any given number of inches from 1 inch up to 33 inches.
Where are these marks placed?
13 inches.
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1 :, 1 6
As an example, I give in the illustration the case of a 13-inch rod with four
markings. If I want to measure 4 inches, I take 1 and 3; for 8 inches, 6 and 2;
for 10 inches, 3, 1, and 6; and so on. Of course, the exact measure must be
taken at once on the rod; otherwise the single mark of 1 inch repeated
a sufficient number of times would measure any length, which would make
the puzzle absurd.