15-Scratch and 24-Scratch
great games for almost anywhere you have a few spare minutes. You don’t
need anything at all to play them, but it helps if you have something to write
on and something to write with.
A more complicated
operations and can entertain people for hours. If you write the numbers from 1
to 100 on a board with space beside each one, students can put up their
solutions over several days.
A magic triangle
numbers 1-6 is simple enough for children who have just become comfortable with
adding single digits. For older students, you can make it more complex by
trying different sets of six numbers. Are there sets of six numbers that won’t
work at all? For a set of numbers that does work, how many different target
numbers can you reach? And for each target number, how many ways can you find
to arrange the six given numbers? This can be played with just paper and
pencil, but it is quicker and more fun if you have numbered counters (or even
just numbered bits of paper).
Bigger magic triangles use nine numbers each, such as the one on the
are some puzzles
involving nine single digits. Ambitious puzzlers might enjoy the challenge of
using two-digit numbers in the triangle once they’ve solved the given
Tired of adding? Try some difference
triangles. Start by finding a single solution for a given size, then try to find
all possible solutions. Again, this puzzle is more fun if you use numbered
counters than if you just use a pencil and eraser. Here are templates for
. (Turn them
upside down to use them.) Once you’ve solved a couple of difference triangles,
you might try using a different set of numbers. Will it work with even numbers?
With odds? What happens if you start at the bottom point and work upwards,
allowing yourself to use any numbers, each one once only?
Baffle your audience by mind-reading! Here is the basic
and here is an
cards if you want to photocopy them on different colours of paper. This game is
actually all about base 2.