Can you create a Latin Square from multiples of a six digit number?
When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
Can you work out how many of each kind of pencil this student
Choose two digits and
arrange them to make two double-digit numbers, for example:
If you choose $1$ and
you can make $12$ and $21$
Now add your double-digit
Now add your single-digit
Divide your double-digit
answer by your single-digit answer.
Try lots of examples. What
happens? Can you explain it?
What happens if you choose
zero as one of the digits?
Try to explain why.
How does it work if you
choose the same digits, for example $3$ and $3$?
What happens if you use
Now choose three digits and
arrange them to make six different triple-digit numbers.
Repeat the steps above: add
the triple-digit numbers, add the single digits then divide the
triple-digit answer by the single-digit answer.
Do you get the same
If you're feeling very
organised, try more digits and see what happens.
investigation is taken from "Numbers in Your Head" by John Spooner,
published by BEAM Education (product code: NYH). It is priced at
£7.50 plus handling and delivery charge. To place an
order, call BEAM on 0207 684 3330. "Numbers in Your Head" is one of
a set of mathematical games books. There are currently three others
in the set ("Casting the Dice", "Cards on the Table" and
"Calculators in their Hands") and in the Autumn term another book
will be added called "A Handful of Coins". The set of five books
(product code GAM1) will cost £35.00 plus handling and