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

Subscribe to get access to the content on this page.

If you are already a Tes/ Tes Scotland subscriber please log in with your username or email address to get full access to our back issues, CPD library and membership plus page.

Not a subscriber? Find out more about our subscription offers.
Subscribe now
Existing subscriber?
Enter subscription number


The guide by your side – ensuring you are always up to date with the latest in education.

Get Tes magazine online and delivered to your door. Stay up to date with the latest research, teacher innovation and insight, plus classroom tips and techniques with a Tes magazine subscription.
With a Tes magazine subscription you get exclusive access to our CPD library. Including our New Teachers’ special for NQTS, Ed Tech, How to Get a Job, Trip Planner, Ed Biz Special and all Tes back issues.

Subscribe now