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BrainDen.com - Brain Teasers # phil1882

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## Everything posted by phil1882

1. i'm not fully sure what you are asking, yes, no object is perfectly identical to another, but that doesn't mean they are necessarily worth less/more. if i have two apples, one shaped like a pear, the other like a cucumber, i still have two apples.
2. your description still doesn't make sense. how can all cuts be both vertical and in any direction and no horizontal. which is it, all vertical (same direction) or any direction?
3. i dont really understand the question. your picture seem contrary to your description. your picture seems to suggest you can cut in any direction, but your description suggests all cuts have to be in the same direction. i'll solve both. for lines in any direction: http://mathworld.wolfram.com/CircleDivisionbyLines.html 1/2*(n^2 +n +2), n=500; 125251 5000000 = 1/2*(n^2 +n +2) n=3162 for cuts in the same direction: each cut adds 1 new region. for 500 cuts, that 501 rejoins to get 5000000 peices 4999999 cuts are needed
4. whoops, legitimately forgot about this topic, sorry guys.
5. count me in, though i may be rather slow in posting.
6. lets do several steps and see if we can develop such a function. 1 H 1 S 1 N 3 H 1 S 2 H 3 S 3 N 9 H 5 S 2 N 12 H 11 S 9 N 31 H 21 S 12 N 54 H 43 S 31 N so here are our rules. Hn = 2*Sn-1 +Nn-1 Sn = Hn-1 +Nn-1 Nn = Hn-1 so, combining we have... Sn = Nn +Nn-1 then Sn-1 = Nn-1 +Nn-2 thus Hn = 2*(Hn-2 +Hn-3) +Hn-2 Hn = 3*Hn-2 +2*Hn-3 so... F(x) = 1 +3x^2 +2x^3 +9x^4 +12x^5 ... 3x^2*F(x) = +3x^2 +9x^4 +6x^5 2x^3*F(x) = +2x^3 +6x^5 F(x)*(1 -3x^2 -2x^3) = 1 F(x) =1/(1 -3x^2 -2x^3) thus it will be the nth term of this series, whatever that is.
7. if i spent a month on it i might be able to do the necessary calculation, don't have that kind of patience though.
8. since it been a couple weeks without even a guess, I'll go ahead and post my answer and see if anyone can do better. i get 59. 0 1 0 2 0 3 0 1 0 3 0 2 0 1 0 3 0 1 0 2 0 1 0 4 0 1 0 2 0 3 0 1 0 3 0 2 0 1 0 4 0 1 0 2 0 1 0 3 0 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0 2 0 1 0 4 0 1 0 ? 51 52 53 54 55 56 57 58 59 60
9. heres an alternate version that i came up with, place the digits 1-n where n is 4 such that no consecutive digit of any step value, starting at step value, repeats. here's an example where n is 2. 0 1 0 2 1 0 2 1 2 0 1 ? 1 2 3 4 5 6 7 8 9 10 11 12 here starting from 1 and going a step of 1, there are no repeats. starting from 2 and going a step of 2, no repeats, and so on. However there is no way to get 12 without repeating. your task is to find the max value for 4.
10. the first rule of fight club is, you do not talk about fight club. there are no rules for how rules are made, with the exception that we try to stabilize and civilize society.
11. i think you mean... x: this number is surrounded by no more than x true statements. what the maximum number of trues you can have, and what would the board look like? here's my attempt
12. it seems to me that T F F T should be 1 2 2 1. if you meant this... 3 2 1 4 1 2 3 3 3 3 3 4 6 4 4 2 3 4 4 3 1 1 2 4 3 cannot be solved. F T start for top left corner T T now 1 doesn't work.
13. i'd say 6. if you take into account letter frequency, the letters to the left of u far outweigh the letters to the right.
14. the strings <<>><><>, <><><<>> are considered equivalent, though for the proposes of uniqueness, i put the factors in order from lowest to highest.
15. correct. one of my questions is about addition. basically my question is, given a number system that uses multiplcation as its basis, (multiplying two numbers in recursive format is just concatenation) an you come up with a method for addition? ill do 7 as an example 7 is prime. < 7 > 7 is the 4th prime so replace the 7 with a 4. < 4 > 4 is composite, its factors are 2 and 2. < 2 2 > 2 and 2 are prime. <<2><2>> the number two is the first prime so cant be reduced further. replace with blank. <<><>>
16. if n is composite, break it into its prime factors, if n is prime, place < > around n and replace n with the nth prime its is. the first 20 numbers then are... 1 <> 2 <<>> 3 <><> 4 <<<>>> 5 <><<>> 6 <<><>> 7 <><><> 8 <<>><<>> 9 <><<<>>> 10 <<<<>>>> 11 <><><<>> 12 <<><<>>> 13 <><<><>>14 <<>><<<>>> 15 <><><><> 16 <<<><>>> 17 <><<>><<>> 18 <<><><>> 19 <><><<<>>> 20 hypothesis: 1) there is no general method for adding recursive numbers. 2) numbers that differ by 1 wont differ in recursive representation by more than 2 brackets 3) symmetric recursive numbers, recursive numbers that can be represented in such a way that they are a mirror image at the middle, grow at a logarithmic rate somewhat similar to the primes. can you confirm or disprove any of these?
17. it seems to me what you really need is an encryption method that can be reversed if necessary but would take longer to reverse than to solve the sudoku yourself and get the same encryption. what do you think of this idea? it may not even require a computer, depending on how difficult the encryption method is.
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