Solving the Dilemma: Taking 2 Different Pills Every Day

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  • Thread starter Thread starter paulmdrdo1
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Discussion Overview

The discussion revolves around a hypothetical scenario involving the administration of two different pills (Pill A and Pill B) under strict conditions. Participants explore potential methods to ensure survival when faced with the challenge of distinguishing between the pills after mistakenly having multiple pills of each type without knowing which is which. The scope includes problem-solving and reasoning related to the scenario.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant suggests adding one Pill A to the three unknown pills and splitting each pill in half to create a balanced dose, expressing uncertainty about the effectiveness of this approach.
  • Another participant agrees with the idea of splitting the pills but emphasizes that doing so could still lead to an imbalance, as it is possible to end up with more of one type than the other.
  • A later reply reiterates the concern about the potential for taking an incorrect combination of half pills, highlighting the risk of consuming too many of one type.
  • Another participant proposes a method of splitting each pill and sharing halves with a friend, aiming to ensure an equal distribution of the pills but acknowledges the uncertainty in identifying which halves belong to which pill type.

Areas of Agreement / Disagreement

Participants express varying opinions on the proposed methods to solve the dilemma, with no consensus reached on a definitive solution. The discussion remains unresolved regarding the best approach to ensure survival while adhering to the conditions set forth.

Contextual Notes

Participants have not fully resolved the implications of splitting the pills, and there are assumptions about the effectiveness of their proposed methods that remain unexamined.

paulmdrdo1
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The doctor told you to take 2 different kind of pills (Pill A, Pill B) for ten days everyday. Both pills look exactly the same (same weight, color, shape, size, etc…;).
If you take more than 1 pill of the same kind per day, you will die. Furthermore, if you do not take 1 Pill A, and 1 Pill B every day, you will also die.
One day, you got distracted and by mistake put 3 pills on the table 2 B pills and one A pill and you don't know which is which.

How can you survive?

I've already searched for the solution to this problem.
Adding 1 pill A to the 3 unknown pills and split each pill in half. Thus having a balanced dose.
Half of those you take and save the other half for the next day.

I still don't get it. Because there is still a posibility that I might take more dose of one pill than the other.

What you think?
 
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Hi paulmdrdo!

So we have 2 pills A and 2 pills B and do not know which is which.
If we take half of each pill and discard the other half, we will have 2 half pills A and 2 half pills B, won't we?
Swallowing all of those gives us 1 dose of pill A and 1 dose of pill B.
 
I like Serena said:
Hi paulmdrdo!

So we have 2 pills A and 2 pills B and do not know which is which.
If we take half of each pill and discard the other half, we will have 2 half pills A and 2 half pills B, won't we?
Swallowing all of those gives us 1 dose of pill A and 1 dose of pill B.

We have 4 pills in total. Splitting each pill into half we will have 4 half B pills and 4 half A pills. Since we don't know which is which, there is a posibility that you might take 3 half pills B and 1 half pill A or 3 half pills A and 1 half pill B or 4 half pills B or 4 half Pills A.
 
paulmdrdo said:
We have 4 pills in total. Splitting each pill into half we will have 4 half B pills and 4 half A pills. Since we don't know which is which, there is a posibility that you might take 3 half pills B and 1 half pill A or 3 half pills A and 1 half pill B or 4 half pills B or 4 half Pills A.
We have a total of $4$ pills. When we divide a pill in half, we keep one half with us and give the other half to our friend. We do this one by one for each pill. In the end we will be left be two halves of pill A and two halves of pill B.
 

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