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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?
Age 11 to 16
Challenge Level
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He would like to put the same number of plants in each of three gardens, planting one garden each day.
On the first day he puts some plants in the shed. Overnight, they double.
The next day he plants some in one of the gardens. The remaining plants double overnight.
The next day he plants some in a second garden, and again the remaining plants double overnight.
On the final day he plants all the remaining plants in the third garden.
Use the interactivity below to help you work out how many plants he should put in the potting shed on the first day, and how many he should plant in each garden.
Can you find more than one solution?
What do the solutions have in common?
Can you find the smallest number of plants he could use?
If you have enjoyed this problem, you might like to move on to More Magic Potting Sheds .
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.