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Prison Escape Puzzle

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An interesting number puzzle I came across recently.

(I have woven the original puzzle into a story - so you won't be able to search for the answer online!)

An innocent prisoner has been locked up behind an impenetrable door with a three digit combination lock, known only to the prison guard and changed every day.  In one week, he will be executed.

The governor takes mercy on him and the prisoner is told that he may write a final letter to his family.  One the day after they receive it, they'll be given one opportunity to tell the prison guard the combination number of the prison cell - if they get it right, the prisoner goes free - if not then he'll be executed.

On the appointed day, the prisoner will be given a box full of plastic numbers: zero through nine - with hundreds of numbers of each kind - and he'll be told the three digit combination lock number that will release him (anything from '000' to '999').   Luckily, the 9's don't look like upside-down 6's!

He must pick out some of the plastic numbers and pass them to the jailer - who will mix them up and give them to his family to help them to figure out how to release him.

So...for example...you might think that if his combination number is 414 - then he could take two 4's and a 1 from the box to give to his family - but because the numbers are mixed up - his family don't know whether it's 144, 414 or 441 - so he'd only have a one in three chance to be free...and that's a risk he cannot take.

The prisoner realises that he can tell his family in advance to add together the numbers he's going to give them and that'll be the combination!  This would actually work...and guarantee his escape!  So you can imagine his elation!


But here's the catch.  The prison guard is on the take - and tells the prisoner that he will demand that the family pay him $1000 for each number the prisoner gives to them.

Worse still, the prisoner suspects that the guard will read the final letter he sends to his family - and he might be evil enough to pick that day's combination to maximise his earnings or even to prevent the prisoner from escaping at all if there is any loophole in the scheme that he proposes!

The prisoner slides into depression - using the 'adding up the numbers' approach, he'll go free - but if the combination number were 993 - then the prisoner would need 110 '9's and a '3'...which would cost his family $111,000 - they could never raise that much money...so he has to come up with a strategy that requires handing over fewer numbers.

What is a strategy that the prisoner can give to his family to (a) absolutely guarantee his escape and (b) minimise their cost?

(NOTE: It's not a trick question - the prisoner hands over some plastic numbers and is released and although it's not cheap - it'll definitely cost his family less than $10,000 no matter what the combination number is)

Post your answers below!



Reader Forum: Prison Escape Puzzle

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From: Archon Shiva  Date: 2017-07-17 20:13:18  

So... solution?
From: Steve Baker  Date: 2017-07-06 13:10:10  

@Archon: I fixed the repeat-posting bug this morning. Looks like quite a few people (myself included) got bitten by it! Thanks for letting us know.
From: Steve Baker  Date: 2017-06-28 05:36:27  

@Archon: Yeah - I should probably try to fix that! Thanks for the report.
From: Archon Shiva  Date: 2017-06-21 13:42:43  

In other news, don't refresh a page if the last thing you did was post.
From: Archon Shiva  Date: 2017-06-21 13:42:17  

Four of the first, two of the second, one of the last.

3-2-1 might work, saving another 1k, but if there are identical numbers it might become tricky.

From: Archon Shiva  Date: 2017-06-21 09:42:11  

Four of the first, two of the second, one of the last.

3-2-1 might work, saving another 1k, but if there are identical numbers it might become tricky.