BrainDen.com - Brain Teasers

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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... ?

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.

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.

9. Making 271

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

Nice analysis! I wish I had thought of that.

17. 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.

19. 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.

24. 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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