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A little brain work

I'm just about to catch a train to sunny Southend for a couple of days of talks, but before I go, I'll leave you with a little brain stretching challenge.


I have two bottles, one containing water and the other containing wine. I pour one measure of wine into the water bottle. I then pour an equal measure from the water bottle back into the wine bottle. At the end, there is just as much water in the wine as there is wine in the water. Which of the following have to be true to make this possible (you can choose more than one):

  • The bottles are the same size
  • The water and wine are thoroughly mixed after the measure is poured into the water bottle.
  • The wine and water have to be thoroughly mixed after the measure is poured back into the wine bottle
  • The wine has the same density as the water
  • The water and wine are miscible


… or is it impossible to be certain that there is just as much water in the wine as there is wine in the water?

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Don't go any further until you've attempted some sort of answer.

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Last chance to consider your answer.

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In fact, none of the conditions have to hold true - there will always be just as much wine in the water as water in the wine. Think of it like this: at the end of the process, the wine bottle holds exactly the same amount as it did initially, so it must have had exactly the same amount of water added to it as wine was removed.

Notice how the way that the question was phrased can distract you from the true facts. Even if you got the right answer, the chances are that the phrasing proved a distraction. You probably worried about partial mixing of water and wine, for example. Sometimes re-phrasing the question is an essential for knowledge gathering and creativity.

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