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## 'Crossings' printed from http://nrich.maths.org/

Tobi and Charles from Luanda International
School both sent in correct solutions to this problem. Some of you
made the mistake of thinking that you could have one stick crossing
all of the rest, but the question did say that there must be
2 sets of
parallel sticks.
Tobi's solution is given
below.

10 sticks:

To find the biggest number of crossings, put 5 sticks going down
and 5 sticks going across so there will be 25.

To find the smallest number of crossings, put 2 sticks going
down and 8 sticks across so there will be 16.

15 sticks:

To find the biggest number of crossings for an odd amount,
instead of splitting the sticks in half split them into the the
closest numbers to half (e.g 7 and 8).

To find the smallest number of crossings do the same as you did
before, put 2 going down and the rest going across.

Estimate for 50 sticks:

For the biggest amount put 25 down and 25 across (625).

For the smallest amount put 2 down and the rest across
(96).

Estimate for any number:

To find the biggest for any number, split the amount in half and
put half across and half down but if its an odd amount split the
amount into the 2 numbers closest to half.

To find the smallest amount put 2 down and all the rest
across.

Charles explains how to find the greatest
number of crossings for an odd number of sticks a different
way.

If the number of sticks is an odd number, then you will have
to divide the odd number of sticks by 2. Then add a half a stick to
the top layer of sticks and take half a stick away from the bottom
layer. After that multiply the two numbers together.