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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"...

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DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Novemberish

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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