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KA-1 News!
I have just realised I have got two ciphers mixed up! The actual message the original cipher should have been is shown below (same keyword, same cipher and only one word changed – so I don’t mind which one you use to submit answers with!):
211010020020222222012102101010222222220102202222222021201210010222222121102020210010012222222100220222222122112011020011122010112201020222222022011110021010112
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Here is KA-1 Hint Four to clear up confusion:
WREIHRLIRGIHKHIIFNTRDISETOARETCFYOHCOIRPEEPDTLW The 10 Digit ‘Tally Number’
=================================
Here is something to amuse yourself with.
This is for your own ‘enjoyment’ do not post answer, you can comment on it if you wish.[0 1 2 3 4 5 6 7 8 9] row 1
[d d d d d d d d d d] row 2Replace the ten d’s in row 2 to form a 10 digit decimal number such that the 1st d under the 0 in row 1 indicates the total number of zeros in the entire number, the d under 1 indicates how many 1’s are in the number, and so on to the last digit whose digit indicates how many 9’s are in the number. (zero is a digit, of course.) This is all in our common base 10.
The answer is unique.Harry, as there is no cipher involved I am not giving you the answer – have a go yourself.
I like that puzzle TLW and I have a solution but I am interested as to whether there may be multiple possible solutions? I can’t think of any way of making a different solution but it feels like there may be one?
You are right Harry but that has told everyone!!! Best Edit it Harry.
It is unique, only base 4 [0123] has two solutions.
If want more to do in this line I’ll post it.
Did anyone see this Additive Alphamatic on Twitter? Hope the link works when this gets put up.
There are 26 solutions in base 10 and 3 solutions in base 9.
——-
STAY
SAFE
+SAVE
=====
LIFESUp through 10, I checked for uniqueness by brute-forcing in C (faster than Python).
After ten, the pattern holds, but checking uniqueness takes too long.
11: 72100001000
12: 821000001000
13: taking too long, but we know it’s 9210000001000re TLW 10-tally:
Here are the answers for bases up to 10:
1210
2020
21200
3211000
42101000
521001000
6210001000
After 5, I see a pattern.@TLW thanks for explicitly saying that you are using base 10, instead of an implicit decinormative assumption that would marginalize the polydactyl extraterrestrial community.
@Harry are you happy to keep edit deleting correct answers?
It would help for those who would like to post prove their answer.[Sure, but I have started letting things through for that one now, because the discussion is getting interesting! Harry]
@67105112104101114
If you want to investigate this with further related challenges let me know and I’ll post more.@Kford, so you used the mixed alphabet on the plaintext side, rather than on the ciphertext side. Even still, F is in the wrong place. [Might be worth checking this, but if that is wrong then do post a rebuttal. I can always edit it! Harry]
TLW The 10 Digit ‘Tally Number’ Continued
============================================
Well here is what I was going to put up but Madness has done it all for you!!
But see further below.Uniqueness was proven in 1968 by Martin Gardner and Edward P DeLorenzo.
I do not have possession of these.You are on your own with the following, don’t ask me for answers or programs to use.
Things for you to do:
Solve for other bases 4, 5, 7, 8, 9 … 36.
Note: No ‘tally number’ exists for bases 1,2,3 and 6.
There are 2 solutions for base 4 the only base to have 2
There is 1 unique solution for all other bases greater than six.[0123] base 4
[dddd]
[dddd]Can you find the general formular for all bases greater than six?
When you have done a few it may become obvious.Daniel Shoham from MIT observed (in 1995) the R2 digits must add to 10 and derived a value for the maximum possible value for each digit in Row 2. His logic was, if digit x appears under digit y there must be x appearances of y, hence x * y < 10.
[0123456789] y
[9943211111] x (maximum y’s)More workings to keep you busy…
Mr Pickover being the innovator of many a math problem added to this.
=======================================================================
All below is in base 10 workings.[0 1 2 3 4 5 6 7 8 9] row 1
[d d d d d d d d d d] row 2Take the answer of row 2 as the start row and solve for that, that answer then becomes the start row and so on.
Can you find a row 3 or row 4?
If so what happens if you continue?R1 = 0123456789
R2 =
R3 =
R4 =
R5 =
R6 =Using any of the digits 0 to 9 in any order, repeats allowed, choose any starting 10 digit number of your choice and, working like above, what is the longest path you can obtain.
Note that there may be more than 1 solution at each step and that means you will have to choose the one that carries the path forward.
The longest path found (in 1995 by Tomas Oliveira e Silva from Portugal) goes to R9 before looping back to R7. He started with R1 = 0000122245
And his longest length -loop- found goes to R5 (and starts over from R1)
Started with R1 = 0000111244Also his longest path not leading to a loop, but to a dead end, given here in full
R1 = 1223334444
R2 = 4223331111 (there are 42 other solutions to 1223334444)
R3 = 0332220000 (there are 4 other solutions to 4223331111)
R4 = 3550003333 (there are 2 other solutions to 0332220000)
R5 = 0555550000 (there is 1 other solution to 3550003333, leading to a loop)
R6 = No solution – dead endIt is currenty (in 1995) not known if there are other paths of the same length.
If there are any other ‘finds’ or anything you else can add to this let us all know.
[TLW: Re the 27t problem.I haven’t seen a post about it yet. Not sure what has happened. Harry]
TLW The 27 Tiles Problem
==========================
This Puzzle consists of 27 tiles.[ 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 ] row 1
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] row 2Row 1 has 3 tiles of each number 1 to 9. (The 0’s in row 2 are just place holders.)
You are to arrange them into row 2 so that there are the same number of spaces
between two tiles of the same value and the space count is the value of the tilee.g. 1*1*1 and 2**2**2
where the * is a space and will be filled with one of the other numbers.
There are 3 solutions (6 counting reversals).
Test yourself – find all three. Good Luck and Enjoy.
Given your 3 answers in the form of a sum (answer + answer_reversed)
No answers for you Harry – do not want to spoil it for you.
I refuse to submit my answers to 27 Tiles in the form answer+reversed, since it is not secure.
So here are the SHA1 sums of the concatenation of the ASCII string “madness” with the string of the
answer expressed as an ASCII string of digits, for the three solutions:cc211bdd7069ea334dbbdac4829254a8a9cd2ad9
9b7a19dee30254c760175ba3dd85d19d3f1f77f3
d130f230f697d1ded58bc936bf5d858ecc47f1a8
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