Choose any three by three square of dates on a calendar page...
Can you explain how this card trick works?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
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.
A Latin Square is an arrangement of numbers in a square in which each number appears exactly once in each row and column. So, for example, the number represented by ? can't be the same as B or *, and * can't be the same as D, ? or @.