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## Quiz of the Month (December 2000)

### Hector C. Parr

***

#### SOLUTION TO LAST MONTH'S QUIZ

```         1) 1, 2, 3

2) (i) 8 cubes have just three painted faces
(ii) 36 cubes have just two painted faces
(iii) 54 cubes have just one painted face

3) 421052631578947368

Notes

1).    1 + 2 + 3 = 6
1 X 2 X 3 = 6
This is the only solution involving positive whole
numbers. (If fractional values are allowed then two
of them can be assigned arbitrarily, and the third
easily calculated. For example: 3, 4, 7/11 )

2). As a check: Number of unpainted cubes = 27.
Then adding, 8 + 36 + 54 + 27 = 125, as expected.

3). Consider the unknown multiplicand ending in 8.
Multiply it by 2 with short multiplication, and
immediately copy each digit of the product into
the multiplicand. The process ends when 8 is
obtained without a corresponding carry digit. ```

#### THIS MONTH'S QUIZ

```  1. What number ending in 8 is multiplied by 3 when the
last digit is transferred to the beginning?

2. John's age and Ken's age add up to 24. John is twice as
old as Ken was when John was half as old as Ken will be
when Ken is three times as old as John was when John was
three times as old as Ken. How old is John now?

3. A clock loses exactly six minutes in 24 hours. If it is
right at noon, what will be the time, precisely, when the
clock next shows 4 o'clock?```

***

(c) Hector C. Parr (2001)

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