So, does Z = 0?

Yes, Z=0. Of course, if you used Z=26, it wouldn't matter because the arithmetic is done mod 26.

(1,1,6,2,2,2) (1,1,7,1,3,3) (1,1,8,1,2,5) (1,2,3,1,2,3) (1,2,5,1,1,8) (1,3,3,1,1,7) (2,2,2,1,1,6)

There are two piles, containing

between 100 and 1000 items. A is

allowed to choose any two items

from the first pile, and B is

allowed to choose any two from

the second pile. If A has only

two-thirds as much choice as B,

how many items are in each pile?

SUPERPRISMATIC'S LAST WALTER

PENNEY PUZZLE: The Den has done

a spectacular job of solving all

but 1 (#40: Un-halving a Message)

of Walter's puzzles. I'm sure

that #45 will be solved. And

I'm willing to bet that you

people are so tenacious that

#40 will also be solved within

a few weeks. I hope you enjoyed

his puzzles. I'll try my best

to make up a few challenging

ones each month or so.

X must belong to the set {2004,2008}.

Edit: made my point clearer.

Is it definitely an 8 second from the end?

With [ 12 2 5 10 10 6 7 9 10 ] I got "Bad news travels fast."

If the numbers are correct, I can get "Bad news travels East," though it doesn't make as much sense.

I looked it up. Walter Penney's written answer has East!

A pair of dice have letters on the

various faces in addition to the

usual spots. One die has the letters

A, L, and V on three faces with N, T,

and W, respectively, on the opposite

faces. The second die has the

letters B, E, and F on three faces

with D, S, and R, respectively on the

opposite faces. The dice are rolled

nine times, with successive throws

being 12, 2, 5, 10, 10, 6, 7, 8, 10.

In the process a certain message is

spelled out. What is the message?

SUPERPRISMATIC CLARIFICATION: On

each throw, you get two letters. Here,

you get to decide which of the two

letters comes first with each roll.

For example, if you find that A and D

came up on the first roll and E and T

came up with the second roll, the

message could begin either of 4 ways:

DAET, ADET, DATE, or ADTE.

Wait never mind I understand, write a sorting algorithm based on the fact that we are sorting 3 items instead of 2 at any given time.

@super ummm how so?

The only way a 3 pan thing can act the way people are answering is if the arm lengths are all the same and the angular distance between arms is 120 degrees. I was thinking of the more general case. Since I never looked at 3-pan puzzles here, I jumped to the wrong conclusions. Sorry.

How can you say a hypothetical isn't true?

And it is totally possible to create.

But can we get some clarification on the question. What are you asking for an efficient sorting algorithm for 3 objects? Are you asking someone to write the function tri(a,b,c)? As far as I can tell tri(a,b,c) is provided. So what are we supposed to sort?

I didn't say a hypothetical isn't true. I just said that a 3 pan balance can balance when the weights aren't all the same.

"for example consider a three way balance scale. you put objects in each of the three levers, and based on the results of the levers, you can tell which objects are heavier or lighter." This just isn't true. If the three moments add up to 0, the thing will balance. There are lots of ways for this to happen even when a, b, and c are all different.

A certain 10-letter word having the

second and fifth letters the same is

treated as follows: the first two

letters are multiplied together

(using the values A=1, B=2, ...,

Y=25, Z=0); then the next two letters

are similarly multiplied together and

the two products added (mod 26).

The sum is reconverted into a letter

using the same correspondence. The

same operations are performed on

letters 2 to 5 producing another

letter. This is continued until the

seventh letter is produced from the

last four letters of the word. The

letters so generated are, in order,

FPSLMMZ. What is the word?

"falty is easy won you is racing places widow or rely vast sat tack the back EU" ...too bad it doesn't make any bloody sense and "faulty" is misspelled - but I give up already.

there must be hundreds of valid words that do fit the pattern - how to find the ones that make sense when strung together?

You can be sure there will be no spelling mistakes in such a puzzle -- it would allow too much leeway. Also, nonsensical combinations of words should be thrown out. When I did this, I began with some pieces of possible text and then guessed at some sensible extensions. Needless to say, it took a long time to come up with something that began to make sense. As soon as I got some nice pieces, extending them got a little easier -- although still difficult. I know it's hard, but I suppose someone on this board will eventually come up with the right sentence.

Bits 1 to 5 of a certain random

binary stream are converted to a

decimal number (from 0 to 31) and

used to encipher the first letter

of a message by mod-26 addition.

Bits 2 to 6 of the stream are used

to encipher the second letter, etc.

The result is

VSYOM ZIUEA GIIWA

XTOBL ITNFX IUBL

[/code]
What is the message?

The fraction 1/N (for a positive

integer N) is found to have a decimal

representation which is cyclic with

period 26. The digits proceeding

left to right from the decimal point,

are assigned in order to the letters

from A to Z. Note that by this

scheme a digit may stand for more

than one letter. The message:

"A cab is a taxi" enciphered by

means of these equivalents becomes:

0 100 54 0 3075. Find N.

I have been thinking about this since it was posted. It seems to me that you could find a corresponding letter that would add up to each number given with any letter you randomly chose. The first number 3 for example; The first letter of the first half could be any letter lets say Q=17 which would have a corresponding letter L=12, 17+12=29 29-26=3. Or H=8, and U=21 8+21=29 29-26=3. Every other letter in the sequence would have a corresponding letter assigned to it in the same fashion.

Meaning you could use any random words or sentence for the first half of the message. The problem is finding the one right combination of the hundreds of thousands of words that would generate a readable full message. With out fully finding the correct corresponding letters to the second half, ie I just made up the second half letters as actually figuring them out would not be a readable sentence anyway, I get the following...

Example 1: "Green tomatoes are like purple yarn b/ajendotjvnwurmcfeutqpxdskeuskrt"

Example 2: "To be or not to be? That is the question. G/vbeomcparwkgmwpctrbeosbfunfldr"

My point being unless I am missing something, are there not just too many possible options for the first half of the message to get the whole thing?

This is really tough. But the actual text is made up of nearly all small words. So, I think the best strategy is to guess some common small words like "the", try it everywhere to see if anything interesting pops up in the other half. Once you get a few good hits, things snowball. That's the way I did it and it took me quite a while working on it sporadically. You could even write a program to try a list of common words and see if you get good letter combinations in the other half of the message.

Some logical assumputions:

1. The letters Y and Z can be eliminated since the largest number is 25 which could potentially be A and X, 1 and 24, but nothing higher.

2. Possible letter combinations are based on the addends, for example, for the number 9, A can only be grouped with H and B can only be grouped with G. For the number 8 A can only get grouped with G and B can only be grouped with F.

Actually, the arithmetic is done mod-26, so if the result is greater than or equal to 26, then 26 is subtracted. So, neither of your restriction rules apply. See Semper Rideo's post above. He gives a good example and only makes one minor mistake which I pointed out immediately.

So if i'm understanding this correctly

to translate each number you need to unmod it, split it, decode it.

so the first letter pair = 3 could be:

3(no mod) -> (1,2) -> (a,b)

29 (mod) -> (3,26) -> (d,z)

. -> (4,25) -> (e,y)

. -> ... -> ...

. -> (14,15)-> (m,n)

. -> ... -> ...

. -> (26,3) -> (z,d)

. (A₁,A₂)

Message = A₁....Z₁A₂....Z₂

Sorry, I don't understand what you're saying.

[Wheels and Words]

I know this is an older one Super, but I've been going back to look at some you've posted. This one for some reason is baffling me. I've got some sort of a blockage in my brain. Maybe's I've been doing too many in a row. What's the technique here?

Well, the wheels are identical. They are just rotated relative to each other to show some word facing the same direction. You are told what can be seen on the wheels at some number of positions later. So, you can get several incomplete sequences, by position, around the scrambled sequence. They must be meshed together to get the partial sequence used for all wheels. If these wheels are set to show you IGYWVHPO, there will be a (possibly partial) word five positions ahead in the group of wheels.

[Coding Challenge]

VXSJ,FUTKOHR,CYQZB,MIEL,WDAN,GP

You are very nearly correct. Two of your subsets can be consolidated in the correct way to get the solution. Nice work!

Does the following correctly exemplify the stated process?

A scanner darkly

a s c a n n e r d a r k l y

1 19 3 1 14 14 5 18 4 1 18 11 12 25

1+18 19+4 3+1 1+18 14+11 14+12 5+25

Encoded message: 19 23 4 19 25 26 4

Edit: forgot the mod 26 function

Yes, except that the penultimate number in the encoded message should be a 0 instead of a 26.

The letters of the first half of a

message are added (mod 26) to the

corresponding letters of the second

half, using the values A=1, B=2,

etc. The result is:

3 10 16 9 22 24 11 23 6 5 24

19 16 7 19 8 22 3 13 19 4 14

3 22 12 18 13 4 14 25 14

[/code]
Read the message.

5 min saved each way so wife picked him up at 4:55, walked for 55 mins

You got the trick of looking at the driver's point of view. Otherwise, things get messy. You've got it!

4076,318952

Nice going!

solving graphically I found

55 minutes

Graphically?

The ten minutes that was saved was obtained from them meeting (her picking him up) earlier than normal. She was able to pick him up early because of the shorter distance she had to drive. This saved distance would be the same both directions and the time saved would be equally split, coming and going. The ten minutes saved resulted from a one way trip that was five minutes shorter.

5 PM minus 5 minutes = 4:55 PM

He walked for 55 minutes.

Yep! Easy when you look at it correctly!

55 minutes.

This is without any calculations, so if this is the right answer, I'll explain why!

Yes! It's very simple when you look at it the right way, isn't it?