superprismatic
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Here's a cute little problem I read in one of Martin Gardner's pieces a while back. When I first tried to work it, I made lots of equations and even more variables and, well, generally botched it! I am paraphrasing Gardners wording of it, so forgive my lack of eloquence. I searched on this site for it without success. If it was never on this site, it certainly deserves to be here! My wife drives me to and from work every day along the same route, both coming and going. I leave work at precisely the same time, 5 PM, that my wife pulls up in the car. One day, my boss let me leave early. I left work at exactly 4 PM. Rather than wait an hour for my wife to get there, I decided to walk along the route that she takes. At some point, she saw me walking, picked me up, did a U-turn, and drove home. I noticed that we arrived home 10 minutes earlier than we usually do. How long had I been walking before my wife picked me up? Assume idealized conditions, i.e., the car trip from home to work takes precisely the same time as from work to home, U-turns and getting into the car are instantaneous events, etc.
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Edit: fixed a typo
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Here's a puzzle inspired by a Walter Penney puzzle which probably requires programming. If anyone can do it by hand, I will tip my hat to him/her/it! A string of letters is produced as follows. The 26 letters are split into some number of disjoint subsets. The elements in each subset are arranged in some order and each has a pointer to its first element. One of the subsets is chosen with probability proportional to its size. When a subset is chosen, the element under its pointer is picked to be the next element of the letter string then its pointer is moved to the next element of the subset. The pointers advance circularly, so a pointer goes from the end of its subset to the beginning of it. This continues until a letter string of the desired length is obtained. The result is: VFXCUMYSQTJWDKOHRZIFUVXTSKOABJ VHCRYXNELFUSWJDQZGTKOBVHCXANRP FUSJYWVQXSDMZTBAIELCYKONHRGPFJ UWTQMZIKEBDOHVRLCGXPFUYANMSIEL GWPDQZJATNVKMBIWXOHRFCUETDLGKP YQOZMHANISREFUJTBKLCVXOSHGJWVY XRDPAFUNMQTKOZIELHBSRGWFJVUPDX MTSKAICJEYQLGPZBMOHRIELNFVXCUT [/code]What are the ordered subsets?
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A string of decimal digits is produced as follows. The 10 decimal digits are split into 2 disjoint subsets A and B. The elements in each subset are arranged in some order and each has a pointer to its first element. A fair coin is now flipped. If heads comes up, the element under the pointer in subset A is chosen and the pointer is moved to the next element of A. Similarly, if tails comes up, the element under the pointer in B is chosen and its pointer advanced. The pointers advance circularly, so a pointer goes from the end of its subset to the beginning of it. This continues until a digit string of the desired length is obtained. For example, suppose A={9,1,2} and B={5,3,8,6,7,4,0}. Then the sequence of flips H,H,T,H,T,H,T,T,T,H will produce the digit string 9,1,5,2,3, 9,8,6,7,1. What would the ordered subsets be if the decimal digit string is 4,3,0,1, 8,9,7,6,5,2,4,3,1,0,8,7,9,6,4,0,7,5, 6,2,3 ?
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You did the problem correctly and as it was designed to be done. It's unfortunate that you thought I meant "point on the bottom" when I said "bowling pin pattern". I'm sorry for this confusion. The only reason I said "bowling pin pattern" was to say that the triangle was filled with circles and not having circles just around the edges. As to how to arrive at the hole pattern first, I don't know how to do that either. Of course one could write a program to enumerate all 12-hole triangles which take out all 36 letters using the 3 orientations, then try each one and look for words. But I don't think that is a viable approach without writing a program. You have a nice explanation of a good way to solve this problem!
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If you are doing this problem "by hand", it's too difficult to look for possible hole patterns -- there are just far too many to consider. However, if you write a program to solve it, this is a good way to go. I don't know what the hole pattern is for this problem, but I'll post it in a week or so if nobody does it first. Perhaps ljb will post it in a spoiler for you. I hope so.
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36 circles are arranged in the form of an equilateral triangle, eight circles to a side. The letters of a message are written in the circles, starting from the top and proceeding from left to right. A triangular piece of cardboard with twelve holes cut out is placed over this and the exposed letters read out. The cardboard is given a 120 degree clockwise turn and another twelve letters read out. A final 120 degree clockwise turn allows the last twelve letters to be read out. The result is: HLRSO CGTBT AITEA OITUH YEYBT EWMNA HERLR D[/code]Read the message. SUPERPRISMATIC CLARIFICATION: The 36 circles are arranged like bowling pins.
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No, not a relative. But I met him a few times. He was kind of like Mr. Burns on The Simpsons. I still have more of his puzzles to put up -- one every day or two for a while.
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Did you make this puzzle up? Now who's gonna to clean up all these cardboard wheels?! I didn't make this puzzle up. It was originally posed by Walter Penney sometime in the 1960s. I have some unpublished papers with lots of his puzzles. I have posted some of my own here, but if I use those made by someone else, I try to give proper attribution.
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There are eight wheels, each bearing the same scrambled alphabet around the rim. These are mounted on a shaft and turned until the word LOVESICK appears. Three positions farther on appears PAYCBLSO. The wheels are then reset to the word DAUGHTER. Four positions farther on appears VZCDSBIY. If the wheels are now reset to IGYWVHPO, what word will appear five positions farther on?
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I'm not sure what you mean but the disks are unchanged from the first message except for the initial orientation of the disks to one another. For the second message, then, you don't know how they are initially rotated relative to one another. The rotation of the outer disk still goes clockwise during encryption.
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It's not arbitrary -- spaces are removed, then the text is enciphered, and then the cypher is put into groups of 5 for easy reading.
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Thirteen of the letters of the alphabet are written around the rim of one disk, the remainder around the rim of another, pivoted to turn relative to the first. Each letter of a message is replaced by the corresponding letter on the other disk. After each letter is enciphered, the outer disk is rotated one position clockwise relative to the inner disk. By this scheme, "Hitch your wagon to a star" becomes: SZRJU INDLU IKALF KQMBL V [/code] Another message, with a different initial placement of the disks, comes out: [code]JLNIW ATUYE EHXFW DMBMT MKPIW WVDU What does it say?
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Thanks, I'm glad you had some fun with this cute little puzzle!
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To get some practice, a student beginning the study of Morse Code listened to transmissions on his short wave set. The sending rate was too fast to allow him to distinguish between dots and dashes, but he was able to count the number of strokes and to distinguish the ends of letters and words. One day last month (December) he copied down the following: 33 4333 443231223 34344223 12344 [/code]Here 1 means either a dash or a dot was sent, 2 means .., or .-, or -., or --, etc. Read the message.
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Nicely done people!
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If you then them, you get the following message: p c a p c w a m a i p e c s o m c s s t t b r s t o p Next thing was to However, I'm drawing blanks as what to do next. Could someone please solve it, or give more hints.
