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superprismatic

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Everything posted by superprismatic

  1. Five encrypted thoughts

    This 324-character message is an encrypted quotation: XPRXWUIWUOLZYXBFTTJMDVOCTTXPPPKLEVROQPRFPLTHWSMOGVCYPG QSIJHIEGYPWFGRAMHXYUMOAAOMGBUYMRJNVXOAVZHIOWFXPTBTZNHL LHKHKLSJSLGKZYFYBUTFTOSFHHMZGRQFELYEKFHWILBDBDROHIZLIM MILZIHORDBDBLIWHFKEYLEFQRGZMHHFSOTFTUBYFYZKGLSJSLKHKHL LHNZTBTPXFWOIHZVAOXVNJRMYUBGMOAAOMUYXHMARGFWPYGEIHJISQ GPYCVGOMSWHTLPFRPQORVELKPPPXTTCOVDMJTTFBXYZLOUWIUWXRPX[/code] which was encrypted in the following simple way: 1. The quotation has been converted to numbers using A=0, B=1, C=2, ..., Z=25. 2. A second stream of numbers is made by reversing the sequence of numbers made in 1 above. 3. These two streams are added modulo 26. 4. The stream produced in 3 above is then converted using 0=A, 1=B, 2=C, ..., 25=Z. The result of all this is the 324-long stream above. Here is an example of encrypting a different quotation: [code]ITHASYETTOBEPROVENTHATINTELLIGENCEHASANYSURVIVALVALUE I T H A S Y E T T O B E P R O V E N T H A T I N T E L L I G E N C E H A S A N Y S U R V I V A L V A L U E 8 19 7 0 18 24 4 19 19 14 1 4 15 17 14 21 4 13 19 7 0 19 8 13 19 4 11 11 8 6 4 13 2 4 7 0 18 0 13 24 18 20 17 21 8 21 0 11 21 0 11 20 4 4 20 11 0 21 11 0 21 8 21 17 20 18 24 13 0 18 0 7 4 2 13 4 6 8 11 11 4 19 13 8 19 0 7 19 13 4 21 14 17 15 4 1 14 19 19 4 24 18 0 7 19 8 12 13 18 0 13 9 4 14 1 9 18 24 7 15 1 21 22 13 0 11 2 6 12 19 1 15 22 15 1 19 12 6 2 11 0 13 22 21 1 15 7 24 18 9 1 14 4 9 13 0 18 13 12 M N S A N J E O B J S Y H P B V W N A L C G M T B P W P B T M G C L A N W V B P H Y S J B O E J N A S N M[/code] The result of this is the 53-long stream: MNSANJEOBJSYHPBVWNALCGMTBPWPBTMGCLANWVBPHYSJBOEJNASNM What is the quotation which has been encrypted to the stream above starting XPRXWUIWUOLZYXBFTTJMDVOCTTX... ?
  2. reversed coefficients

    One possibility you hadn't addressed: What about roots which are 0, and possibly with multiplicity?
  3. Dueling cards

  4. How big was the dinner table?

    I have one question which could make a big difference. It's a bit indelicate, so I'll put it in a spoiler.
  5. Dueling cards

  6. reversed coefficients

  7. The kindest (shortest) cut of all

    @Bonanova or anyone else who may have an interest in this: Do you have a proof that that circular arc is the shortest? Conceivably, a piece of a trigonometric curve, or exponential curve, or another conic section may be shorter. The possibilities are endless.
  8. Making 271

    I'll bet that the answer is divisible by 7.
  9. Birthday Probability

    Nice analysis! I wish I had thought of that.
  10. Factor this

  11. Magic octagon

  12. Magic octagon

  13. Unlocking doors

  14. Unlocking doors

    I have 2 questions: 1. Are we to find keys to open all 61 doors? A door need not be locked for us to test a key to it. Or are we to find keys for only the 60 locked doors? 2. If the basement is technically the eleventh floor, then there must be 10 floors above it with 10 rooms per floor. That's a total of 100 rooms plus the office in the basement. Is this correct? If so, shouldn't each above-ground floor have 6 rooms? Otherwise, there would have to be 40 rooms without doors.
  15. Factor completely over integer coefficients

  16. Greeting Time

    no, that is 00:00:34 the minute zeros lit as LL Do they always do that? Do the hours also do that sometimes? I think the mechanics of it all should be explained.
  17. Stick a round

  18. Numerus Primus Dividus

  19. Unfaithful wives

  20. Unfaithful wives

  21. A tossing game you sure win

    This type of game is widely known as "Penney's Game". The Penney is Walter Penny who made quite a few puzzles in the 60's and 70's. I posted nearly 50 of his puzzles (from unpublished papers of his) a few years ago on this forum. You can look at some of them if you search for Penney on this site. They are quite clever puzzles!
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