5th May 2006 at 01:00
Seven up

Choose only from the digits 1, 2, 3, 4, 5 and 6

123 is a three-digit number such that no two digits sum to 7.

How many different numbers can you find such that no two digits sum to 7 and no digit is repeated?

How many can you find if a digit may be repeated?

Old measures

Clues across

1 Noggins in 3 pints

2 Trusses in 1 load

4 Square yards in 4 square poles

6 Furlongs in half a mile

7 Yards in 1 mile

9 Cubic inches in 1 cubic foot

10 Yards in 1 furlong

12 Pints in 6 gallons

13 Inches in 6 fathoms

Clues down

1 Yards in 2 poles

3 Weight in pounds of 8 bushels of water

5 Pounds in 1 hundredweight

8 Pounds in half a stone, ounces in half a pound, quarters in half a hundredweight

9 Square inches in a square foot

11 Cubic feet in 1 cubic yard

SOLUTIONS Seven up There are 48 numbers if each digit is different. Listing the numbers systematically, there are 6 choices for the first digit, four for the second and two for the third, giving 6 X 4 X 2 = 48 numbers. There are 78 numbers if a digit may be repeated, 30 with a repeated digit: 6 in which the 3 digits are the same; 24 in which 2 are the same.

SOLUTIONS Old measures (ages 10-14) Some internet research may be needed here. Two useful websites are: www.eppo.go.threfUNIT-ALL.html and en.wikipedia.orgwikiimperial_unit

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