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Quiz of the Month (June 2002)
Hector C. Parr
SOLUTION TO LAST MONTH'S QUIZ
1. The following seven weights are sufficient:
1, 2, 4, 8, 16, 32, 64.
For example, to weigh 77 g,
77 = 64 + 8 + 4 + 1
2. The following five weights are sufficient:
1, 3, 9, 27, 81.
For example, to weigh 52 g,
52 = 81 - 27 - 3 + 1
3. At his first move A leaves 496 counters.
Then whatever B removes, at his next move A can leave 485.
Then whatever B removes, at his next move A can leave 474.
(And so on, coming down in steps of 11)
At his final move A leaves 1 counter, forcing B to lose.
THIS MONTH'S QUIZ
1. The wheel of a locomotive (excluding the flange) has diameter 2 m, and the width of the flange is 5 cm. When
the locomotive is travelling at 100 km/hr, what is the speed relative to the track, and the direction of motion,
(a) the highest point, A, of the flange, and
(b) the lowest point, B, of the flange ?
2. A ship's propeller shaft is turning at one revolution per second. It is supported in a roller bearing, with cylindrical rollers. The inner race has diameter 20 cm and the rollers each have diameter 2 cm. How long does a roller take to make one revolution and return to its original position ?
3. In question 3, if the inner race were fixed and the outer race were turning at one revolution per second, how long would a roller take to make one revolution ?
(c) Hector C. Parr (2002)
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