New Scientist Enigma 969 – Same From All Angles
by Susan Denham
From New Scientist #2124, 7th March 1998
For the purposes of this Enigma I shall define a “palindromic angle” as one whose n umber of degrees is a whole number less than 180 and is such that the number remains the same if its digits (or digit) are written in reverse order.
I have drawn an irregular hexagon and a line across it in a similar fashion to the one shown here, however the given picture is not to scale. In my figure, the eight marked angles are different palindromic angles, and in fact more than two of them are acute.
What (in increasing order) are the six angles of my hexagon?
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Brian Gladman permalink123456789101112131415from itertools import combinations, permutationspa = tuple(x for x in range(1, 180) if x == int(str(x)[::-1]))for b, c in combinations(pa, 2):a = b + c - 180if a in pa and a not in {b, c}:for c5 in combinations(set(pa).difference({a, b, c}), 5):if a + sum(c5) == 720:c8 = c5 + (a, b, c)ac = sum(1 for x in c8 if 0 < x < 90)if ac > 2:print(tuple(sorted(c5 + (a,))), (b, c))
