7 Days of Christmas: Day 4

Today, for day 4, I’ll be discussing the Gin and Tonic Problem.

Let’s suppose we’ve got a glass of gin and a glass of tonic. Then, you take a 40ml shot of the tonic and pour it into the gin. Afterwards, you take a 40ml shot of the tonic/gin mixture and pour it into the tonic. Is there now more gin in the tonic or tonic in the gin?

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Although you may think that since we added a mixture of tonic and gin, there is less gin in the tonic cup than tonic in the gin cup, the answer is actually that there is the same amount of tonic in the gin cup as there is gin.

Why?

  • You added 40ml of tonic to the gin cup.
  • Then, you took 40 ml of that mixture and poured it into the tonic cup.
  • So, that second shot contained x ml of tonic and 40 – x ml of gin. Therefore, there are 40 – x ml of gin in the tonic cup.
  • Since you poured 40 ml of tonic into the gin cup, but took back x ml, there are 40 – x ml of tonic left in the gin cup.

To read day 3, click here.

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