Take A Break

As a break from the mind-stewing agony of trying to win the accumulator, try this. No prize, just glory. ** ADDED Jan 2 2005: now there IS a prize: £38 **

A number of men (more than one) are in a room.

Each man has either a single large dot on his forehead or no dot.

The men are told that at least one of them has such a dot.

They are told that each man must decide, when he is ready, whether or not he has a dot.

Once he has decided that he has a dot, he must leave the room the next time a bell rings.

After a long time a bell rings once and then rings once again every minute.

Note: The men use just observation and logic, no trickery (mirrors, feeling the dot, signals between them, and so on…) is involved.

Your challenge: write or flowchart a set of precise instructions that, if followed by all the men, would result in each of them deciding accurately whether or not he has a dot.

The winner is the creator of what I think is the most elegant solution. My decision is final.

If you already know the answer, don't spoil the fun - yet.

To extend the fun, please respond by email rather than posting here: jim@bin.co.uk

rgds Jim

Any interest Jim?

Simon

Any interest Jim?

Simon

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Not a sniff, Santa - er - Simon.

Are you going to have go yourself?

rgds Jim

Not a sniff, Santa - er -  Simon.  Are you going to have go yourself?

<{POST_SNAPBACK}>

As I'm sure you can appreciate this is a very busy time for me.

Regards,
Simon

OK Jim's put up £38 for the 'dot on the head' competition, see here:

http://www.saferpak....topic=742&st=40

Jim will post further details, closing date etc.

Regards,
Simon

Thanks, Simon

I suggest we run this until the end of January and then see where we are.

Replies to be sent to me at jim@bin.co.uk - not to be posted here. I will respond to each one

Have fun! And I wish everyone a wonder-full 2005.

rgds Jim

Thanks, Simon

I suggest we run this until the end of January and then see where  we are.

Replies to be sent to me at jim@bin.co.uk - not to be posted here. I will respond to each one

Have fun! And I wish everyone a wonder-full 2005.

rgds  Jim

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Only a week or so to get your entries in. Remember there's £38 up for grabs.

Regards,
Simon

Jim,

Any more entries yet?

We had fun doing this one in our office with each person coming up with a different solution.

We had fun doing this one in our office with each person coming up with a different solution.

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Did you get the right answer? Did you send anything to Jim? Jim are you with us?

Simon

I did send Jim an answer but I'm not telling you his comments yet.

Jim I'm going to close this competition off on Friday 18th February 5.00 p.m. GMT. Please let me know the winner or where you want the prize money to go.

Thanks,
Simon

Jim I'm going to close this competition off on Friday 18th February 5.00 p.m. GMT.  Please let me know the winner or where you want the prize money to go.

Thanks,
Simon

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Sorry to be so late coming back, Simon.

Yorkshire submitted this answer:

1 Count the dots on other peoples foreheads.
2 Use the following table to decide when to leave the room:

Bell number Number of dots seen
1 .............................. 0
2 .............................. 1
3 .............................. 2
4 .............................. 3
5 .............................. 4
x .............................. x-1

3 When someone leaves the room stay where you are

This is very good but I think it falls down in the detail.

Example: assume I have no dot and I see two dots originally. On the second bell, those two - following the same instructions - will leave the room. When the third bell goes, if I follow the instructions to the letter, I too will leave.

So I stayed put (as instructed) when they left the room on bell 2. And on bell 3 I left because I'd counted two dots.

However, since there was a grand total of ... wait for it .... one entry, I suggest the prize goes to Yorkshire.

The model answer, by the way, is:

Before the bell rings for the first time, count the total number (n) of forehead dots you can see. Leave the room when the bell rings for the (n+1)th time, unless anybody left when the bell rang previously.

rgds Jim

Thanks Jim, did anyone get it correct? BTW what shall I do with the rest of the cash?

Regards,
Simon

Jim,

Sorry to be picky but you missed my last instruction

3 When someone leaves the room stay where you are

Jim,

Sorry to be picky but you missed my last instruction

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No, I took that into account.

I stayed put (as instructed in your point 3) when they left the room on bell 2.

But then, on bell 3, I used the table and left anyway because I'd counted two dots and no-one else left at that time.

But, anyway, Simon, I suggest Yorkshire gets the prize - it was a good entry.

rgds Jim

It just shows how careful you have to be when writting instructions for a process.

To me it was quite clear but it is obvious that it wasn't.

Thanks Jim for the Audit.

Yorky send me your address and I will send you a cheque for £38.

Regards,
Simon