Sunday Times Teaser 3180 – Taking the Chair
by Victor Bryant
Published Sunday September 03 2023 (link)
There were eight people on the committee: four men — Jingo, King, Ling and Ming, and four women — Sheena, Tina, Una and Vina. They had to choose a chairperson from among themselves and so each of them voted for their choice, each person choosing someone of the opposite sex. Jingo’s choice’s choice was King. Also, Ling’s choice’s choice’s choice was Sheena. Furthermore, Tina’s choice’s choice’s choice’s choice was Una.
Just two people got fewer votes than their choice did. After further discussion the woman with the most votes was made chairperson.
(a) Who was that?
(b) Who voted for her?
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BRG permalink1234567891011121314151617181920212223242526272829303132333435363738394041424344454647from itertools import productfrom operator import countOf# map leading letters to namesf2n = {n[0]:n for n in 'Jingo King Ling Ming Sheena Tina Una Vina'.split()}men, women = 'JKLM', 'STUV'# men's votes for womenfor mv4 in product(women, repeat=4):# women's votes for menfor wv4 in product(men, repeat=4):# the people's choicespc = dict(zip(men + women, mv4 + wv4))# J's choice’s choice was Kif pc[pc['J']] != 'K':continue# L’s choice’s choice’s choice was Sif pc[pc[pc['L']]] != 'S':continue# T’s choice’s choice’s choice’s choice was Uif pc[pc[pc[pc['T']]]] != 'U':continue# find the votes for each candidatevotes = {c:countOf(pc.values(), c) for c in men + women}# only two people got fewer votes than their choiceif sum(votes[v] < votes[c] for v, c in pc.items()) != 2:continue# find the maximum vote cast for a womanmax_v = max(v for p, v in votes.items() if p in women)# look for all women with this maximum (we need exactly one)wmx, *r = [p for p, v in votes.items() if v == max_v and p in women]if not r:cs = ''.join(p for p, c in pc.items() if c == wmx)f, s, l = str.rpartition(', '.join(f2n[c] for c in cs), ', ')fs = ' and '.join((f, l))print(f"{f2n[wmx]} elected with votes from {fs}.")
