Sunday Times Teaser 2492 – No Title

by Victor Bryant

Published June 27 2010 (link)

I started with a rectangular piece of paper and made a cut across it, dividing it into a triangle and a pentagon. Then I discarded the triangle and measured the lengths of the sides of the pentagon, all of which were whole numbers of centimetres.

I remember that the lengths of the shortest two sides were 17cm and 19cm, and that the length of the longest side was 33cm.

What were the lengths of the other two sides?

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from collections import defaultdict
from number_theory import pythag

# store pythagorean triangles up to a side length of 33
c2ab = defaultdict(list)
for a, b, c in pythag(34):
  c2ab[c].append((a, b))

# consider rectangles of width w and height h
for w in range(17, 34):
  for h in range(17, w):
    # and possible triangles
    for c in c2ab.keys():
      for a, b in c2ab[c]:
        for u, v in ((a, b), (b, a)):
          # form the sides of the pentagon
          d, e, f, g, hh = t = tuple(sorted((w, h, c, w - u, h - v)))
          # and check that its two shortest and its longest
          # sides match the given values
          if (d, e) == (17, 19) and hh == 33:
            print(f'Answer: {f}, {g} [rectangle ({h}, {w}), '
                  f'pentagon {t}, triangle ({a}, {b}, {c})]')

from collections import defaultdict

from number_theory import pythag

# store pythagorean triangles up to a side length of 33

c2ab = defaultdict(list)

for a, b, c in pythag(34):

c2ab[c].append((a, b))

# consider rectangles of width w and height h

for w in range(17, 34):

for h in range(17, w):

# and possible triangles

for c in c2ab.keys():

for a, b in c2ab[c]:

for u, v in ((a, b), (b, a)):

# form the sides of the pentagon

d, e, f, g, hh = t = tuple(sorted((w, h, c, w - u, h - v)))

# and check that its two shortest and its longest

# sides match the given values

if (d, e) == (17, 19) and hh == 33:

print(f'Answer: {f}, {g} [rectangle ({h}, {w}), '

f'pentagon {t}, triangle ({a}, {b}, {c})]')

Sunday Times Teaser 2492 – No Title

by Victor Bryant

Published June 27 2010 (link)

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