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?
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
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