Beach Day by Rodger Bliss
December 2022

Coffee or Tea

Imagine you have one cup of tea and one cup of coffee.

Place a spoonful of the tea into the coffee and then place a spoonful of the tea/coffee mixture back into the tea.

Does the cup of coffee now contain more tea, or the cup of tea more coffee or are they the same?

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8 guesses to Coffee or Tea

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  • Nanao Ise

    I think that the coffee would contain more tea, as compared to the tea and coffee.

    When you take a spoonful of the tea-coffee mixture, you give the tea some coffee – let us say, half?

    However, in giving a bit of coffee to the tea, you lose some coffee from the original coffee cup.

    So proportionally, while both have approximately half a spoonful of the other mixture inside it, the coffee has the same amount of tea in less coffee.

    Then again, you are imagining it.

  • cooffe would have more tea

  • Dude

    OK, both of you are incorrect. Keep guessing.

    (Because there are only three possible answers, please explain how you came up with your answer.)

  • If we can assume the liquids mix completely upon introduction, then they are the same. –
    1 cup = 48 teaspoons
    step 1- coffee has 48:1 ratio of coffee:tea, tea remains pure at 47 teaspoons.
    step two- teaspoon from coffee cup has 48:1 ratio of coffee:tea comprised of 48/49 teaspoon of coffee, and 1/49 teaspoon of tea, leaving coffee with 47 and 1/49 teaspoons of coffee, and 48/49 teaspooons of tea. Teacup now has 47 and 1/49 teaspoons of tea, and 48/49 teaspoons of coffee.

  • Unles, of course, you use a teaspoon to take tea from a to b, and a coffeespoon (One Coffee Spoon is equal to 0.500093505864 Teaspoons) to take mixture from b to a, in which case more tea is left in b than a receives in coffee.

  • Dude

    You are correct, Jimmy Barcus. They are the same! If each cup contains 100 units of its respective beverage and a spoon holds 10 units, then at the start we have:
    CoffeeCup = 100 Coffee
    TeaCup = 100 Tea
    We now transfer a spoonful of tea across to the coffee to give:
    CoffeeCup = 100 Coffee + 10 Tea
    TeaCup = 90 Tea
    We now transfer a spoonful of the coffee/tea mixture back to the tea cup, this 10 unit spoonful will contain [10 x (100 Coffee + 10 Tea) / 110]. So we will have:
    CoffeeCup = 100 Coffee + 10 Tea – [10 x (100 Coffee + 10 Tea) / 110]
    TeaCup = 90 Tea + [10 x (100 Coffee + 10 Tea) / 110]
    If we simplify this we get:
    CoffeeCup = (10000 / 110) Coffee + (1000 / 110) Tea
    TeaCup = (10000 / 110) Tea + (1000 / 110) Coffee
    So there is as much coffee in the tea cup as there is tea in the coffee cup!

    You are today’s winner.

  • Laurence Stein

    The final ratios are always the same. You can simplify the calculation by using the absurd case: The volume of the spoon is equal to the volume of the cup. In this case the final ratios would be 50:50…. or you can do all the math for a spoon volume that are less than a cup volume and just get tired.

  • Paul Ikeda

    The answer is that there is just as much tea in the coffee cup as there is coffee in the tea cup.

    In my opinion, there is a much more simple and intuitive explanation than those given so far as to why this is true.

    It’s clear that both cups start and end up with exactly 1 cup of liquid before and after swapping teaspoons.

    Therefore we can conclude that what ever volume of coffee that is missing from the coffee cup must be replaced with exactly the same volume of tea from the tea cup and vice-versa.