Enigma 1307 - KO, OK?

Enigma 1307 - KO, OK? New Scientist magazine, 18 September 2004. by Susan Denham.

Sixteen players numbered 1 to 16 entered a men's knockout tennis tournament. In each round the numbers of the remaining players were drawn at random to decide who played whom.

At the end of the tournament each player wrote down the number or numbers of the players he had competed against, in the order in which he had played them. The lists of the two finalists had their numbers in increasing order.

Also, each player worked out the total of the numbers in his list. The highest total was four times the lowest.

Which two players were in the final?

Ciao,

Brilliant! And the only solution posted to this Enigma so far. Usually you folks are all over these things, but responce has been a bit slow to this one. Have you been preoccupied thinking about who to vote for? :^)

Nice work (and correct of course).

Ciao,

It was difficult - I normally complete the puzzles first time round (ie in the Magazine) and at the time I thought about this one for entire tube ride home (st james's park to chigwell). I was working on the minimum maximum of individual finalists - never clicked to do the games of both.

There have been moans that the NS Enigma are too easily brute-forced and it is nice to see one that was answered in about 20 lines that were/ could have been done by hand.

I agree with your comment - Brilliant.

Regards

Matthew Newell

Perhaps the problem is that the most obvious way to solve most Enigma problems is computer search, that the program is simple enough to implement, and they are small enough that the brute force method would work.

On this puzzle, the brute force approach wasn't obvious (consider all 16! permutations and assume the right-hand player in any match won), had a large number of cases (16!), and the program would have taken a decent amount of skill to write, so it was easier to think it out.

I did write the progam and it took a fortnight to run on a p4/1.7GHz. Mind you, it was only written in an old version of MS compiler BASIC.

I started from the final and worked my way back to the round of 16.

Ciao,