Games are a bottomless reservoir of puzzle brainchild . This is because games and puzzles both lean to be founded on a concise stage set of ordered rules . This week ’s puzzle headache one of the elementary scheme games ever prepare : tic - tac - toe . Do n’t feel too assured , though . You may be a tic - tac - toe expert , but have you ever tried to play it backwards ?
Did you miss last workweek ’s puzzle ? tally it outhere , and find its solution at the bottom of today ’s article . Be heedful not to read too far ahead if you ’re still working on that mystifier !
Puzzle #2: Reverse Tic-Tac-Toe
citation to Alain Brobecker for creating this neat mystifier .
The tic - tac - toe stance above was reached in a secret plan between two unflawed histrion , stand for neither of them ever made a move that would allow their opposition to win by force play and neither of them miss an chance to force a win themselves . What were the last four moves played ?
While playing tic - tac - toe , the yesteryear is irrelevant . The move you make in any given position never depends on how you touch that status . So it ’s impressive that a stable diagram from a biz where the past does not matter can have the last four moves unambiguously determined . This is the guinea pig of retrograde analytic thinking puzzles ( or “ retros , ” for those in the know ) , which demo a position from some biz and demand you to infer something about the chronicle of the secret plan . Bromus secalinus is the grandad of the retro genre . Its set rules provide for stupefying constructions like the positionhere , which ask you to determine the last 96 move ! convergent thinker must dust off trace evidence from long - gone events , like a palaeontologist infer dinosaur diets from scratch marks on fossilized tooth .
Image: Photo: Shutterstock Graphics: Vicky Leta
While I adore chess puzzles of all types ( and have composed a few retros myself ) , I am unlikely to feed them here for the foreseeable future because I would n’t need to alienate readers who do n’t play . For a delicious institution to cheat retros , determine out Raymond Smullyan ’s account book , The Chess Mysteries of Sherlock Holmes .
We will stake the resolution to the tic - tac - toe teaser next Monday along with a new mystifier . ( Update : you may find this week ’s root and the conform to week ’s puzzlehere . ) Do you know a great puzzle that you think we should cover here ? Send it to us:[email protected ]
Solution to Puzzle #1: 10 Bags of Coins
Last week’spuzzleasked you to discover counterfeit coins with a one - time use shell . The primal idea in the solution is to include a different number of coins from each bag in the weighing . Let ’s start by label the bags 1 through 10 arbitrarily . We ’ll place one coin from bag 1 on the scale of measurement , two coin from base 2 , three coins from bag 3 , and so on , ending with all 10 coin from handbag 10 . If you did n’t puzzle out the puzzle , pause for a moment and ask yourself how you would deduce which bag holds the counterfeits from the resolution of this particular weighing .
We can reason through it this way : what would the graduated table presentation if every coin weighed 1 gram and there were no pseudo ? Adding the one coin from the first bag , two coins from the second bag , etc . , yields 55 grams ( sceptic can fit my gist ) . So if we expect 55 grams with no counterfeit , what would the scale say if the heavier coins go on to live in bag 1 ? We only included one coin from traveling bag 1 in our deliberation , so swapping a undivided 1 - gram coin for a 1.1 - Hans C. J. Gram coin would increase the 55 g to 55.1 grams . What if bag 2 fall out to hold the heavier coins ? Then our 55 grams would get to 55.2 grams because the two coins from dish 2 would now each contribute 0.1 excess grams to the total weight . This continues so that , no matter which old bag contains the juke , the shell shows a predictably different weight . In fact , the digit after the decimal degree say you exactly which bag is the perpetrator ! ( Technically , if it ’s grip 10 , then the free weight would be 56 gm . )
There is a whole , racy world of coin - weighing teaser . They all take exception solvers to find counterfeit coins with a special number of advisement , but they typically ask a balance scale that only tells you whether the coin in one dish are heavier or lite than those in the other ( or equal ) . This puzzle is special in that you get a proper numeric scale leaf but the minimal possible number of weighings . I also see the solution particularly elegant .
Graphic: Jack Murtagh
Did you solve thefirst Gizmodo Monday Puzzle ? Was it too hard ? Too well-to-do ? Just right on ? We would love to hear your feedback as we continue to influence the future of this series !
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Graphic: Jack Murtagh
