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# ABCDCBA

### #1

Posted 06 June 2014 - 05:24 AM

At the aforementioned cinco de mayo party, k-man took only imperceptible offense at

Y-san's mainly-innocent comment. But he did retire brieflly to the library to concoct

some good-natured revenge on the lady. Returning moments later to the main room

he found her in conversation with Rainman, and he put to them a puzzle of his own:

I've put a number into a sealed envelope here, he said, and it looks like this.

And he showed them the sequence * ABCDCBA*. But of course my copy has numbers

for the letters, he explained.

I'm going to tell Y-san the sum of the seven digits, and I'll tell Rainman their product.

Bonanova is not the only one who can resurrect an old puzzle form - you may already

have seen puzzles of this type. It will be helpful if you have. You can discuss

what you know between yourselves, but be careful not to disclose too much.

First to come up with my seven-digit number gets a coveted bonanova gold star.

Then k-man added, here's a clue: 9 >= * A *>=

*>=*

**B***>= 0. and 9 >=*

**C***>= 0.*

**D**

**Y-san** spoke first, to Rainman: I have only a faint clue about what your number is.

I have an even worse idea of what yours is, **Rainman** replied, this is difficult.

I know, **Y-san** mused. At this point, your number is still uncertain.

**Rainman** replied, now I know k-man's number!

What is it?

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #2

Posted 08 June 2014 - 10:38 AM Best Answer

### #3

Posted 09 June 2014 - 03:04 AM

Nice work.

But since Rainman knows the product, he knows at least one of these is not the right number.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #4

Posted 09 June 2014 - 09:14 PM

Nice work.

But since Rainman knows the product, he knows at least one of these is not the right number.

Since, Rainman knows the product, he doesn't even have to think about the other number. This doesn't change the fact that there are indeed two answers to your problem.

Or, am I wrong in stating that there are two possible answers to your question?

### #5

Posted 10 June 2014 - 12:12 AM

I think there is only one answer. Here are the details of what I did. See if I missed something.

In any event, I'm marking the puzzle solved. Good work.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #6

Posted 10 June 2014 - 01:45 AM

I think there is only one answer. Here are the details of what I did. See if I missed something.

Spoiler for Gory details.

In any event, I'm marking the puzzle solved. Good work.

First of all, thanks for the star. Its been decades since I got one

Now,..

### #7

Posted 10 June 2014 - 08:54 AM

Just occurred to me. Did you permit zeros?

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #8

Posted 14 June 2014 - 09:52 AM

Yes Bonanova, I did not permit zeros as I thought in that case Rainman would have given a different initial reply (that he can never find out Y-San's product)

### #9

Posted 14 June 2014 - 09:02 PM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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