Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Magic Potting Sheds

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 .

## You may also like

### Adding All Nine

### Double Digit

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

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 .

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!

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?