Quarterly October 2004 - Odfjell

The Odfjell Quarterly Brain TeaserThe treasure onWabble IslandOn the very small and remote Wabble Island live two kinds of people;half the inhabitants are wibblers and the rest are wobblers. They look,move and sound just the same, but for one important difference: thewibblers always tell the truth whilst the wobblers always lie. An ancientmyth tells of a grand treasure being buried somewhere on the island, andone day a treasure hunter, Fan Oddbow, arrives on the island to try tofind it. However, before starting to excavate Mr. Oddbow wants to knowwhether there really is a treasure or not, a fact to which the natives areall familiar. The Wabble Chief has allowed him one question only, towhatever person he chooses to ask. The problem for our friend Fan isthat although the islanders understand English perfectly, a strict tabooforbids them to use non-native words. Hence, when asking them a yes/noquestion, they reply ‘Zil’ or ‘Ding’. The trouble is that neither we nor ourfriend Fan know which of ‘Zil’ or ‘Ding’ means yes and which means no.And here finally we arrive at this issue’s brainteaser: How can FanOddbow in just one single question establish whether there is a treasureon Wabble Island? Remember that he does not know whether hisrespondent is a truth-telling wibbler or a lying wobbler, or what ‘Zil’ and‘Ding’ really means.We await your solutions, by November 15th at the very latest. And asusual, to qualify you will have to indicate the reasoning behind youranswer. Good luck!Solution to the previous Odfjell Quarterly Brain Teaser:In the summer issue the problem was to establish whether Anna or Barbara started servingin the first set, which Anna won 6 - 3. Five of the games were won by the player who didn’tserve. There are several ways to reach to correct solution, and below we offer a somewhatmathematically oriented solution:Let’s call the player serving in the first set P and her opponent Q. Nine games were played,thus P served in five games and Q in the remaining four. Assume P won x of the games sheserved and that she won y of the games she didn’t serve. Hence, P lost 5-x of the games sheserved, and consequently, Q won 5-x of the games she didn’t serve. The sum of games wonby the player not serving is y+(5-x), which according to the problem equals 5. Hence: y + (5-x)= 5, which gives x = y. The means that P won x+y = 2x games. This is an even number, andhence, Anna, who were the only player winning an even number (6) of games, must be P.Conclusion: Anna served in the first game.We have received eleven suggestions for solutions, which perhaps may not seem too bad.However, seen in context with the total number of readers (4,000 copies, each read by onaverage 1.6 (or so) persons) the response rate is ridiculously low. Nevertheless, praise andhonour to the six persons who submitted correct solutions. We also send somewhat morelimited applause to the two (both from Houston) who sent the correct answer (Anna), butfailed to provide a reasonable explanation why. Again we had to draw the winner, andthis time the prize and praise go to Ronaldo Gimenes, Odfjell Brasil in São Paulo. Parabéns,Ronaldo!odfjell quarterly 19