# phil1882

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1. ## Dvds for Christmas

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.

alright thanks good to know.

the strings <<>><><>, <><><<>> are considered equivalent, though for the proposes of uniqueness, i put the factors in order from lowest to highest.

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. <<><>>

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?
6. ## Prove that you solved sudoku

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 yourselfand 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.
7. ## 11 Letters

doorenownly is the best i could com up with.

i'd say its

11. ## Triangle with a given perimeter

no clue on this one, you can divide a single line segment to any measurement, but showing any point m to construct a triangle of any parameter? much much harder i think.
12. ## numbers by the book

alright sorry, i tried to make it such that there was only 1 solution but looks like i failed. thanks for finding all 3.
13. ## if a,b,c, and d are natural numbers revisited.

yeap, or more specifically a power of 3.
14. ## if a,b,c, and d are natural numbers revisited.

i'm not going to list how to make each weight, however
15. ## numbers by the book

this solution doesn't work, as tim and fred both end in 2. the numbers 1-5 should appear once in each digit place between men, as hint #2 tries to explain.