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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Magic Potting Sheds

Age 11 to 14 Challenge Level:

It may be useful to keep a record of your trials.

Try working backwards from the number of plants in the last garden (remembering that you must always have whole numbers of plants in the gardens and shed).

Can you have an odd number of plants in each garden? (Look at the last garden.)

Describing the different stages algebraically may be helpful.