What would be the smallest number of moves needed to move a Knight
from a chess set from one corner to the opposite corner of a 99 by
99 square board?
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
An excellent explanation of a solution was presented by Andrei
LAZANU Age: 12 School: 205, Bucharest, Romania. I have tried to add
some diagrams to help his text, although I think that it might not
be the case that this works for all triangles. Perhaps someone
would like to think about exceptions?
Well done Andrei.
I used this month's clues to solve the problem. Triangle A from
the triangle fits in the rectangle because:
Now, I see a rule, for fitting any triangle into a rectangle.
It can be made in the following way:
Now, I finished with the rectangle. I search for a method to fit
the pieces of the triangle into a square.
The area of the rectangle is 0.5h*b , which must be equal to
s2 . So, the side of the square is $s =
Because I have already shown how it is possible to transform the
triangle into a rectangle, now, for the transformation of the
triangle into a square I use the previous transformation.
Because the clues helped me a lot, I shall use the figure.
Now, the following step is to show that these 5 pieces, A, B,
C, D and E fit into the square.
The general method to obtain the square from a triangle is