[ASK] Exact Measure Using Two Bottles

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Discussion Overview

The discussion revolves around a problem of measuring exactly 4 liters of water using two bottles with capacities of 5 liters and 3 liters. The focus is on exploring various methods to achieve this measurement, along with the potential to measure other integer volumes of water using the same bottles.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant outlines a step-by-step method to measure 1 to 8 liters using the 5-liter and 3-liter bottles, detailing specific actions for each measurement.
  • For measuring 4 liters, the participant suggests filling the 5-liter bottle and transferring water to the 3-liter bottle until it is full, then stopping after a specific step to achieve the desired measurement.
  • Other measurements (1, 2, 3, 5, 6, 7, and 8 liters) are also described, with each method relying on filling, transferring, and emptying the bottles in various sequences.
  • Another participant expresses appreciation for the provided solution and recalls a previous interaction with the contributor on another forum.
  • There is a brief exchange about the contributor's presence on various forums, including non-math ones.

Areas of Agreement / Disagreement

Participants generally agree on the methods proposed for measuring different volumes of water, but there is no explicit consensus on the best approach or any alternative methods that might exist.

Contextual Notes

The discussion does not address potential limitations or assumptions in the methods described, nor does it explore the mathematical implications of the measurements.

Who May Find This Useful

Individuals interested in problem-solving with practical applications of measurement, particularly in mathematical contexts or recreational mathematics.

Monoxdifly
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Someone wants to take 4 liters of water, but he only has two 5-liters and 3-liters bottles. How is he able to measure 4 liters with only those bottles?
 
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You can in fact make any integer 1–8 litres of water using just those two bottles.

1 litre:
  • Fill up the 5ℓ bottle, and use it to fill up the 3ℓ bottle.
  • Empty the 3ℓ bottle, and transfer the contents of the other bottle to it.
  • Fill up the 5ℓ bottle again, and use to top up the 3ℓ bottle.
  • Empty the 3ℓ bottle, and fill it up again with the contents of the other bottle. There will now be exactly 1 litre of water in the 5ℓ bottle.

2 litres:
As for the 1-litre scenario, but stop after the first step. There will be exactly 2 litres of water in the 5ℓ bottle.

3 litres:
Just fill up the 3ℓ bottle.

4 litres:
As for the 1-litre scenario, but stop after the third step. There will be exactly 4 litres of water in the 5ℓ bottle.

5 litres:
Just fill up the 5ℓ bottle.

6 litres:
Fill up the 3ℓ bottle, empty it into the 5ℓ bottle, then fill up the 3ℓ bottle again. There will be a total of 6 litres of water in both bottles.

7 litres:
As for the 1-litre scenario, but after the second step just fill up the 5ℓ bottle. There will be a total of 7 litres of water in both bottles.

8 litres:
Fill up both bottles.
 
Last edited:
Thanks, Olinguito!

Btw, I have remembered when I saw you in another forum. When I was browsing old threads at MIF, I saw your account there.
 
Yes, I’m on various forums (including some non-math ones). (Nod)
 
Which non-math forums are you in?
 

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