Sunday Times Teaser 2654 – Square Cut

by Andrew Skidmore

I started with a rectangular piece of paper one metre long and more than half a metre wide and used a single straight cut to divide it into a square and a remainder.

I took the remainder and cut it in the same way to produce another square and a remainder. I did this repeatedly until the remainder was itself a square.

As a result the original rectangle had been divided into six squares whose sides were all whole numbers of centimetres.

What was the width of the original piece of paper?

2 Comments Leave one →

brian gladman permalink


# the initial length of the rectangle in cm
length = 100
# try widths of the rectangle greater than 50 cm
for width in range(51, 100):
  # divide the rectangle into a square and a
  # remainder up to five times
  l, w, cnt = length, width, 0
  while cnt < 5:
    l, w, cnt = max(l, w), min(l, w), cnt + 1
    l -= w
  # if the remainder is a square
  if w and l == w:
    print('The original width was {:d} cm.'.format(width))

# the initial length of the rectangle in cm

length = 100

# try widths of the rectangle greater than 50 cm

for width in range(51, 100):

# divide the rectangle into a square and a

# remainder up to five times

l, w, cnt = length, width, 0

while cnt < 5:

l, w, cnt = max(l, w), min(l, w), cnt + 1

l -= w

# if the remainder is a square

if w and l == w:

print('The original width was {:d} cm.'.format(width))

ahmet cetinbudaklar permalink

Drawing squares of axa , axa , axa , (3a)x(3a) , (3a)x(3a) and (7a)x(7a) we get:

(7a)x100=49x(a^2)+9x(a^2)+9x(a^2)+a^2+a^2+a^2=70x(a^2) giving us the value of a hence the answer as 7a

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Sunday Times Teaser 2654 – Square Cut

by Andrew Skidmore

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