How Many Socks Must a Blind Man Take to Guarantee a Matching Pair?

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Discussion Overview

The discussion revolves around a logical puzzle concerning the minimum number of socks a blind man must select to guarantee a matching pair, as well as specific conditions for matching colors. The scope includes logical reasoning and mathematical considerations related to probability and combinations.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that selecting 5 socks guarantees at least one matching pair due to the limitation of colors available.
  • Another participant argues that to ensure a 'dark' matching pair, more than 7 socks must be chosen, as 7 could potentially all be light socks.
  • A further claim is made that selecting 10 socks would be necessary to ensure a matching pair, based on the reasoning that two must be of the same color in any selection of three.
  • There is a question raised about the interpretation of the number of yellow socks, specifically whether it refers to pairs or individual socks, indicating a need for clarification.
  • Another participant reiterates the need for clarity regarding the number of yellow socks, emphasizing that the original post states it clearly.
  • One participant provides a breakdown of the yellow socks, confirming that it refers to three individual yellow socks.

Areas of Agreement / Disagreement

Participants express differing views on the minimum number of socks required for matching pairs, with no consensus reached on the exact numbers. Additionally, there is confusion regarding the interpretation of the number of yellow socks, leading to further questions rather than agreement.

Contextual Notes

The discussion highlights potential ambiguities in the problem statement, particularly regarding the definitions of sock quantities and colors, which may affect the reasoning applied by participants.

tommybell
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I have below logical quiz but can not seem to find a reasonable answer.
Any comment or help will be appriciated.

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A blind man has a draw of socks with 2 dark blue socks, 3 yellow socks, 2 brown socks, and 4 white socks randomly scattered. He has an important function and wants to wear matching socks so decides he will select a number of socks and stop at a sighted friends house on the way that can help him select a matching pair for the function.

1. What is the least number of socks he need to take to his friend’s house to ensure he has a matching pair?


2, What is the least number of socks he needs to take to his friend’s house to ensure he has a ‘dark’ matching pair?


3. Our blind friend is given two more socks, both the same dark blue colour, that he adds to the draw. The next day he is in the same predicament, an important function and he wants to have matching socks. How have the answers to questions one and two changed? Why?

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1. If he chooses 5 socks, then is ought to have a pair since you cannot have 5 different colors of socks.

2. If he chooses 4 + 3 = 7 socks, they could all be light. He thus needs to choose more. If he chooses 7 + 2 = 9, the the two extra could be of different color. So that gives us 7 + 3 = 10, since in 3 selections, two have to be of the same color.

3. See above; everything said still applies, nothing changes.
 
Last edited:
A question... what do you mean by say 3 yellow socks?

is it 3 pairs of yellow socks or just 3 single socks?
 
mubashirmansoor said:
A question... what do you mean by say 3 yellow socks?

is it 3 pairs of yellow socks or just 3 single socks?

It says it clearly...
 
Werg22 said:
It says it clearly...

So... which one? :confused:
 
mubashirmansoor said:
So... which one? :confused:
1 single yellow sock + 1 single yellow sock + 1 single yellow sock = 3 yellow socks.
 

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