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# Guess 1 out of 100 numbers

18 replies to this topic

### #1 Muktombu

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Posted 04 November 2013 - 07:56 PM

Hello all,

I have come across an incredibly difficult riddle which I would like to share with you:

100 people are assigned with natural numbers between 1 and 100. These numbers are entirely random and independent of one another, meaning there can be duplicates (and consequently missing numbers). Each person receives an anonymous list of 99 numbers representing everyone else's numbers but not her own.

She then makes a guess regarding her own number based on the numbers she sees and the strategy that was agreed upon in advance by the group. They cannot communicate in any way and cannot hear what others have guessed, i.e. they are completely isolated all the way through.

The strategy they develop should guarantee that at least 1 person makes a correct guess regardless of the given numbers.

I have battled through this brain crushing puzzle, and would be glad to see your ideas and thoughts.

Cheers!

Btw, I am sorry if this riddle was already posted, I tried searching before posting.

Edited by Muktombu, 04 November 2013 - 07:57 PM.

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### #2 superprismatic

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Posted 04 November 2013 - 11:54 PM

You're correct that puzzles with a similar solution have been on this forum before.

Spoiler for a little hint if you want one

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### #3 phil1882

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Posted 05 November 2013 - 01:49 AM

hmm. i don't see a solution myself either.

with 2 people for example, you have 4 possible results

A B

1 1

1 2

2 1

2 2

at best each person can eliminate half, leaving 1 result uncounted for.

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### #4 phil1882

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Posted 05 November 2013 - 03:02 AM

Spoiler for two

now to try to figure out 3.

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### #5 flamebirde

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Posted 05 November 2013 - 04:14 AM

Spoiler for doubt it, but

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### #6 phil1882

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Posted 05 November 2013 - 06:10 AM

no doesn't work.

Spoiler for

Edited by phil1882, 05 November 2013 - 06:10 AM.

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### #7 phil1882

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Posted 05 November 2013 - 08:37 AM

one possible solution for 3

Spoiler for

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Posted 05 November 2013 - 12:11 PM

Spoiler for what am i missing

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### #9 phil1882

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Posted 05 November 2013 - 02:15 PM

you can have duplicates.

so everyone can be 1 for example.

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Posted 06 November 2013 - 02:07 AM

you can have duplicates.

so everyone can be 1 for example.

help me understand this sentence: "Each person receives an anonymous list of 99 numbers representing everyone else's numbers but not her own."

it reads to me, that a person would have a list of numbers that excludes the number they have.

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