Perhaps you
are an expert at Fruit Ninja, slashing fruits mercilessly with precision using your
much-feared finger. Now can you do the mathematical
equivalent below?

**Question**

**Solution**

We would be
getting nowhere fast if we took a random approach. We are only allowed two slashes. Let us look at the question for more
clues. We have a 5
by 6 grid, giving a total of 30
cells. The total number of parts
in the ratio is 1 + 2 + 3 + 4 = 10. 10
parts correspond to 30 cells, so each part is 3
cells. So the number of cells in
each portion are 3, 6, 9 and 12.

Note that
if we pair up 3 with
12 and 6
with 9, we have
15 cells each. We can just slash
the grid down the middle to achieve this.

We now need
ratios of 1 : 4 and 2
: 3 for the remaining parts. We certainly can achieve this if we were
allowed two more slashes and if we used horizontal lines, like this:

However, we only have one more slash. Can we make this slash do the work of the two
horizonal slashes? Yes! Replace the two horizontal slashes with a
single slanting slash that passes through the mid-points of the horizontal
slashes. This gives four trapezia. The reason why it works is because for each
portion, an extra triangular area is added but it is offset by the removal of a
triangle of the same area, like this:-

We can check that the ratios of the areas of the
portions are as required. Done!

H02. Use a diagram / model

H04. Look for pattern(s)

H05. Work backwards

H08. Make suppositions

H09. Restate the problem in
another way

H11. Solve part of the problem

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