This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Here is a solution to Calcunos from Ned who
has just left Christ Church Cathedral School in Oxford and is about
to go to Abingdon School. Adam of Swavesey Village College,
Cambridgeshire also sent in some good work on this
I have solved your question from the July challenges, CalcuNos,
as there being 1,374 methods. The numbers of lightbars for each
So we only need to consider combinations which add up to 16
using the numbers 2 to 7 and no others.
There are 32 ways of making 16.
The number of lightbars is unique except for three numbers which
have 5 bars and three which have 6, so it is necessary to work out
the number of different ways of arranging each set of numbers and
then multiply by three for each of the 5's or 6's involved in the
7, 6, 3: the 3 could go in one of 3 places, the 7 in one of 2
(one has been taken up by the 3) and the 6 in one of 1; this makes
However, as the 6 can represent any one of three numbers, one
must multiply by 3, making a total of 18 combinations for numbers
whose digits contain 7, 6 and 3 lightbars.
For combinations like 6,2,2,2,2,2 one sees that, as the 2's must
be all the same, only 6 combinations exist (622222, 262222, 226222,
222622, 222262, 222226) times three (for the six), making 18 for
The numbers of combinations for each set of numbers are:
This gives a grand total of 1,374 numbers which, on a
calculator, have 16 light bars.