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Quiz of the Month (January 2001)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

```         1) 2758620689655172413793103448

2) 15

3)      4 hours, 1 and 1/239 minutes
or  4 hours, 1 minute, 60/239 seconds

Notes

1). Take the unknown number (ending with 8), multiply
it by 3, and copy each digit of the product into
the multiplicand. Stop when 8 appears in the
product without a carry digit.

2). J + K = 24
J = 2(K - x)          (x years ago)
J - x = 0.5(K + y)    (y years hence)
K + y = 3(J - z)      (z years ago)
J - z = 3(K - z)

Solving, J = 15, K = 9, x = 1.5, y = 18, z = 6

3).    1434 clock minutes = 1440 real minutes
So  240 clock minutes = 240 X 1440/1434 real minutes
= 241 and 6/1434 real minutes
= 241 and 1/239 real minutes.

```

THIS MONTH'S QUIZ

```  1. What is the smallest number (greater than 1) which
leaves a remainder of 1 when divided by 2, by 3, by
4, by 5, by 6, by 7 and by 8?

2. What is the greatest possible number of occasions during
a year (not a leap year) on which a Friday falls on the
13th day of a month, and in which months do they occur?

3. The following multiplication sums are correct, but some
of the numbers have got lost. Fill in the missing numbers.

(i)      *1*9             (ii)           ****
X     *                        X     *3
*2*87                           *****
=====                          8*575
******
======
```

***

(c) Hector C. Parr (2001)

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