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A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

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Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

Latin Numbers

Age 14 to 16
Challenge Level

 

1st                     
           
3rd 4th 5th      2nd
           
           
           

Work out the number in the pale blue cell first:

If the bottom row is 6N, what can you deduce about the first digit of N?

Work out the numbers in the column marked "2nd":

If the fifth row is 5N, what can you deduce about the last digit in that row?

What can you say about the last digit of 2N, 4N and 6N?
What can you deduce about the last digit of the first row?
Will it be even or odd?

The first digit of N will appear as the last digit in one of the other rows.
Multiply different possible values for the last digit of N and see which gives you the results you are looking for.

Once you have completed the right hand column you'll know which numbers will fill the column marked "3rd".

After completing the column marked "3rd" try to complete the column marked "4th"...