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Skyline
I’ve said elsewhere that the pieces of a puzzle should have some sort of mathematical completeness, and that a puzzle should be fresh and new. This month’s Puzzle of the Month turns those two rules on their heads, along with several others. For example, pentominoes are an ideal puzzle as there are five pieces formed from all the ways of joining 12 squares together, whole edge to edge. This puzzle, which I think is called Skyline, probably designed by Jean-Claude Constantin, is neither original, being just another checkerboard-style puzzle, albeit seven units a side, nor mathematically complete as the pieces are a fairly random set of 2, 4, 5, 5, 5, 6, 6, 7 & 8 units.
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However it is a truly delightful example of the puzzle designer’s art. It is beautiful and eye-catching at first glance. Closer inspection shows a fine bevelled base, with a low fence along each side to retain the 9 pieces. Then we come to the pieces themselves. An uninspired designer might have settled for planar polyform pieces, but here we have pieces designed to look like city blocks, with towering peaks of varying heights, some flat-topped and others sloped at 45 degree angles. The overall concept of a city skyline is completed by using four different woods, heightening the irregular appearance of the whole puzzle. This clearly means that the pieces, delightful to examine and hold in the hand, are not flippable.
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Mathematicians reading this may have noticed that the 9 pieces total 48 units, leaving an apparent gap. What is this gap? A demolition site? Building in progress? A car park? The designer’s oversight? The observant viewer may have noticed an aluminium chimney soaring skyward through the other buildings. This takes the place of the 49th unit, slotting neatly into a depression in the base. The remaining nine pieces must be fitted around the ‘chimney’. The final glory of this puzzle is that there are actually 13 depressions to take the chimney, giving the puzzler 13 different challenges. To protect the designer’s copyright I have not pictured all the pieces, just enough to give the general idea.
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