An unconventionalmini crossword puzzle
A full - sizedcrossword with a tricky theme
A new computer code breaking puzzle calledDecipher
Photo: Maryna Babych (Shutterstock)
I also write aseries on numerical curiositiesfor Scientific American , where I take my favorite mind - blowing ideas and stories from math and present them for a non - math interview . If you enjoyed any of my preambles here , I promise you plenty of intrigue over there .
Keep in touch with me on X@JackPMurtaghas I continue to sample to make the Internet grave its head .
Thanks for the fun , Jack
Solution to Puzzle #48: Hat Trick
Did you survivelast week’sdystopian nightmare ? Shout - out to bbe for nailing the first puzzle and to Gary Abramson for ply an impressively concise answer to the 2nd teaser .
1 . In the first puzzle , the group can guarantee that all but one mortal hold up . The person in the back has no information about their hat colour . So alternatively , they will use their only guess to communicate enough entropy so that the remaining nine the great unwashed will be able to deduce their own hat color for sure .
The person in the back will count up the number of red hats they see . If it ’s an odd bit , they ’ll cry “ red , ” and if it ’s an even number , they ’ll scream “ low-spirited . ” Now , how can the next person in line of reasoning deduce their own lid color ? They see eight lid . Suppose they count an peculiar number of bolshy in front of them ; they know that the person behind them saw an even issue of Bolshevik ( because that person shouted “ blue ” ) . That ’s enough information to deduce that their hat must be red to make the entire figure of reds even . The next person also know whether the person behind them watch an even or odd number of red hat and can make the same deductions for themselves .
2 . For the 2nd puzzle , we ’ll present a scheme that guarantees the whole group survives unless all 10 hats happen to be red . The group only needs one someone to gauge right , and one wrong guess mechanically kill them all , so once one somebody guesses a color ( declines to slide by ) , then every subsequent individual will authorise . The finish is for the blue hat closest to the front of the line to guess “ blue ” and for everybody else to exit . To accomplish this , everybody will pass unless they only see red hats in front of them ( or if somebody behind them already guessed ) .
To see why this works , observe the person in the back of the line will pass unless they see nine reddened lid , in which case they ’ll reckon gamey . If they say blue , then everybody else fleet and the group wins unless all ten lid are red . If the person in back passes , then that signify they go out some blue chapeau forward of them . If the second - to - last person sees eight bolshy in front of them , they know they must be the blue lid and so guess blue . Otherwise , they pass . Everybody will happen until some person towards the front of the crinkle only sees scarlet hats in front of them ( or no hats in the case of the front of the communication channel ) . The first person in this post guesses gloomy .
The probability that all 10 hat are red is 1/1,024 , so the mathematical group wins with probability 1,023/1,024 .
Daily Newsletter
Get the best technical school , science , and civilisation intelligence in your inbox day by day .
News from the time to come , delivered to your nowadays .
