You may also like  problem icon    problem icon   Consider
numbers of the form un = 1! + 2! + 3! +...+n!. How many such
numbers are perfect squares?  problem icon   Investigate
sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for
different choices of the first two terms. Make a conjecture
about the behaviour of these sequences. Can you prove your
conjecture?  Summing Squares   You may wish to make six copies
of each square prism below to aid you in visualising the problem
that follows. 1 by 1 by 1, 2 by 2 by 1, 3 by 3 by 1 cuboids If I
take six of the red cubes I can make this 3 by 2 by 1 cuboid: 3
by 2 by 1 cuboid I want to surround this with blue cubes to make
the 5 by 3 by 2 cuboid below:  5 by 3 by 2 cuboid Could I build
this cuboid by adding on six blue square prisms like the one
above without splitting any of them? If so, describe how to do
it. If not, explain why not, and describe how to arrange the
blue square prisms so that as few as possible need to be split.
I want to surround this with pink c