### More Mods

What is the units digit for the number 123^(456) ?

### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

### Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

# Latin Numbers

##### Stage: 4 Challenge Level:

Here is an example of a 4 by 4 Latin square:

Can you see what is going on?

In a Latin Square each symbol or colour occurs exactly once in each row and exactly once in each column.

In the grid below, N is a 6 digit number with a very special property:
if you double the number and write it in the second row,
treble the number and write it in the third row,
and so on...
you end up with a Latin Square!

Can you find the six digit number N?

If you're finding it difficult to get started, click below to see a diagram showing one possible order in which you can work out each value.

Work out the number in the pale blue cell first.
Then the numbers in the column marked "2nd", then "3rd" and so on...

 1st 3rd 4th 5th 2nd

There is some more advice in the Getting Started section.