perplexus.info :: Just Math : Deciphering the Duel

Deciphering the Duel (Posted on 2024-03-09)

After the Math Department’s Magic: the Gathering tournament, the five competitors told their colleagues how it turned out. But, mathematicians being what they are, each competitor told only a half-truth: that is, one true and one untrue statement. Here’s what they said:

Allen: Deis came in second. I finished third.
Black: I won the whole thing, and Chang finished second.
Chang: I got third place; poor Black was last.
Deis: I was in second place, and Frayer was fourth.
Frayer: I ended up fourth. Allen was the champion!

What were the true results?

No Solution Yet Submitted by Danish Ahmed Khan

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computer solution

| Comment 2 of 3 |

clearvars

orders=perms('abcdf');

for i=1:length(orders)

order=orders(i,:);

if sum([(order(2)=='d'),(order(3)=='a')])==1

if sum([(order(1)=='b'),(order(2)=='c')])==1

if sum([(order(3)=='c'),(order(5)=='b')])==1

if sum([(order(2)=='d'),(order(4)=='f')])==1

if sum([(order(4)=='f'),(order(1)=='a')])==1

disp(order)

disp([(order(2)=='d'),(order(3)=='a')])

disp([(order(1)=='b'),(order(2)=='c')])

disp([(order(3)=='c'),(order(5)=='b')])

disp([(order(2)=='d'),(order(4)=='f')])

disp([(order(4)=='f'),(order(1)=='a')])

end

finds

dcafb

0 1

1 0

indicating the order was

Deis, Chang, Allen, Frayer, Black

and Frayer's first statement was the true one; everyone else's last statement was their true one.

Posted by Charlie on 2024-03-09 12:29:50

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