# Enigmatic Code

Programming Enigma Puzzles

## Tantalizer 418: Life in the old dogs

From New Scientist #968, 25th September 1975 [link]

Once a year one-legged parrot-fanciers gather from all over Britain to take part in the Long John Silver Memorial Chess Tournament. Each entrant plays one game against each other, scoring 2 points for each win, 1 for each draw and 0 for each loss. The victor gets 16 men on a dead man’s chess board (yo ho ho) and a bottle of rum.

This year a record 1081 games were played. Each entrant totalled a different number of points, finishing ahead of everyone younger than himself. No one totalled an odd number of points. No two players were the same age.

George was the youngest player to win a game with the King’s Gambit and Henry the oldest to lose one with the Slav defence. All those who played the Slav defence finished ahead of all who played the King’s Gambit.

What was the result of the game between George and Henry?

[tantalizer418]

### One response to “Tantalizer 418: Life in the old dogs”

1. Jim Randell 6 November 2019 at 7:14 am

If there are n players and each player plays a game against every other player, then there are T(n – 1) games played in total.

We are told there were 1081 games played, and T(46) = 1081, so there were 47 players.

There are 2 points awarded per game, so 2×1081 = 2162 points awarded in total.

Nobody scored an odd number of points, and the total of the first 47 even numbers is:

0 + 2 + … + 92 = 2(0 + 1 + … + 46) = 2 T(46) = 2162

So this tells us the sequence of points, (0, 2, 4, …, 92). And this also orders the players in age order.

The player who scored 0 points lost all 46 of their games.

The player who scored 2 points, won only one of their games, which must be the game against the player with 0 points.

The player with 4 points, must have beaten the player with 0 points and the player with 2 points.

And so on, each player won exactly the games against the players earlier on the list (and hence younger) than them.

Henry played a game with the Slav defence, so must have finished ahead of George (who played the King’s Gambit), so must have beaten George in the game between them (and also must be older than George).

Solution: Henry won his game against George.

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