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'Different by One' printed from http://nrich.maths.org/
Take two rod colours, say light green (3 units) and yellow (5
units) - as many as you like of each colour.
Make a line of greens and a line of yellows so that the lines
differ in length by one (a white rod)
Now try with other colour combinations. For example blue with
purple - you'll want to try lots of combinations.
Keep a record of your results.
What do you notice ? Why does it happen ?
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The longest rod (orange) is 10 units long but we do not have to
stop at 10. You can have a blue-yellow rods (length 14 units) and
orange-black rods (17 units long) for example.
Six blue-yellow rods and five orange-black rods make lines that
differ by one (white)
Once you think you have spotted what happens for a difference of
1, try a difference of 2, using plenty of different colour
Especially notice the cases where a difference of 2 can be
achieved but a difference of 1 cannot.
Record, notice and explain what happens.
What about other differences ?