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Quiz of the Month (August 2007)
Hector C. Parr
SOLUTION TO LAST MONTH'S QUIZ
1. 5 5/143 mins. past 12 and 60/143 min. past 1.
2. 26 62/143 mins. past 3 and 17 29/143 mins. past 5.
N.B. Strictly speaking, if the answers are to be exact they
must be expressed as vulgar fractions.
1. Suppose the pointer positions are respectively x min. and
y min. past the hour.
It can be seen that x and y cannot lie in the same 5-minute
sector, so take x between 0 and 5, y between 5 and 10.
The minute pointer moves 12 times as fast as the hour pointer.
So taking y as the minute pointer, y = 12x
and taking x as the minute pointer, x = 12(y-5)
Solving, x = 60/143, y = 5 5/143
2. y = 12(x - 15)
x = 12(y - 25) (etc.)
3. There is one solution within any pair of 5-minute sectors.
There are twelve 5-minute sectors.
So number of pairs of sectors = 12*11/2 = 66
© Hector C. Parr (2007)
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THIS MONTH'S QUIZ
In the following display
notice that: (i) each row contains a 3-digit number,
(ii) the number in row 2 is twice that in row 1,
(iii) the number in row 3 is three times that in row 1,
(iv) each of the digits 1 to 9 occurs once only.
Find three other examples of 3-digit numbers which can
replace row 1 above, such that the four conditions (i),
(ii), (iii) and (iv) can again be satisfied.
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