1. ## Got a match?

Person A removes an undisclosed number of matches from a matchbox, and gives them to a referee for safe keeping.
A hands the remainder to person B and offers this challenge:

"Take as many matches as you want from the box and place them on the table in front of you, in an arrangement similar to the attachment (showing an example for six matches).
I will then ask the referee for the matches he is holding, and I will place these matches next to your arrangement, thereby doubling the number you see on the table."

A wins every time. How is it done?
I'll issue clues as answers to specific questions.

Alan

2. ## Re: Got a match?

Would binary come into this somewhere?

3. ## Re: Got a match?

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">There were only 2 matches in the match box!</span hide>

4. ## Re: Got a match?

There are two possible answers to your question, Leif. So I suppose binary does come into it. But you're obviously on the right track.

Alan

5. ## Re: Got a match?

That would work for that case only. A can make it work for all cases.

Alan

6. ## Re: Got a match?

<P ID="edit" class=small>(Edited by Leif on 19-Jan-05 11:57. To clarify my answer having re-read the question!)</P>
On the basis the answer is binary based, <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">the direction the match faces represents either a 1 or a 0. To 'double' the number, the pattern has an additional '0' match added to the right hand side, thus doubling the number shown</span hide>.

7. ## Re: Got a match?

That's a valid solution Leif. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">I hadn't thought about the "sense" of the match's direction - I assumed they'd all be seen as 1s. But the method will work for any binary number. To the right of the line of matches, </span hide>
A adds 4 matches in the following pattern:

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