bout de papier, Vol. 7, No. 3 (1990), p. 48
“Fiendishly clever, Liebnitz,” rasped Chief MacBannock. “Our long-time enemies in the East Bloc, their domestic and foreign policies in tatters after recent events, have been experimenting with new forms of diplomacy. If this catches on, we may all be out of a job. It’s bad enough with peace breaking out all over.”
“What exactly is going on, Chief?” replied the ace logician.
“They’re testing out a method of settling diplomatic disputes by carrying out fixed-term negotiations and having the results adjudicated by outside observers. Points are awarded for winning each negotiating match, and at the end of a given series, a “top nation” prize is awarded. The East Bloc countries are still playing their first series, and we managed to get a copy of the standings so far — here, look at this paper.”
“Well, when telling us that the Dogmatians had 5 points, he added that one other country had the same score. Motley also noted that one other country besides Etcetera had an exact balance between SNEs FOR and AGAINST.”
“That should do it, Chief!” smiled Liebnitz, and proceeded not only to fill in the gaps in the table, but also to give MacBannock the results (countries plus scores) of each negotiating match played so far. Can you duplicate this double feat?
Matches SDNES SDNEs
Country Played Won Lost Tied For Against Points
Anxieta 1 5 3
Bylatea 2 2 4
Coruptio 1 3 4
Dogmatia 3 7 5
Etcetera 1 8 8
“Unfortunately, Motley (our agent in Grappa where the series is being held) spilled ouzo all over his only copy of the table and so only some of the entries remain legible. We’re hoping you can fill in the rest for us. Let me explain the system. The first column here is MATCHES PLAYED — that is, completed. We know that each country will play each of its competitors once; we also know from Motley that only one country has completed all its matches. The next three columns are simple; they just reflect how many of the matches played so far have been WON, LOST or TIED by each team. The last column reflects POINTS accumulated by each country to date, on the basis of 2 points for a win, I point for a draw and no points for a loss.”
“What is an SDNE, Chief?” asked Liebnitz.
“Motley says that it stands for Stiff Diplomatic Note Equivalent, which is their way of scoring the negotiations. Each successful manoeuvre — say an unusually Machiavellian backstab, some truly outrageous grandstanding or a piece of creative ambiguity so impenetrable as to make Kevlar look like tissue paper — is awarded a value in SDNEs, and comparing the two SDNE scores at the end of the match decides the outcome. These scores reflect only the completed matches, of course. Motley indicates that most of the matches have been close, with only one being decided by two SDNEs (the score was 5-3) and the rest by one. He adds that two of the matches have been tied, one scoreless and the other 1-1.”
“Did Motley have any other information, Chief? I have almost but not quite enough for the solution.”
Hints for solution
In solving puzzles of this kind, it is useful to note the following: (a) since everyone plays everyone else exactly once, the maximum number of MATCHES PLAYED for any player is one less than the total number of players; (b) the total number of MATCHES PLAYED must be even, since each match is counted twice – once for each participant; (c) since each match results in two points (either both to the winner or one each in case of a tie), the total number of POINTS must equal the total under MATCHES PLAYED; (d) the total number of WINS must equal the total number of LOSSES, by definition; (e) the total number of TIES must be even, since two countries take part in each; and (f) the total number of SNEs FOR and AGAINST must be equal, since the cycle of matches is closed
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Originally published in bout de papier, Vol. 7, No. 3 (1990), p. 48. Read the rest of this issue →
