Untitled

Cup Enigma
Coffee and Tea

(The solution given for the coffee and tea enigma does not seem to explain its reasoning well enough so I made this page to explain it better.)

Ok, here is how the enigma goes: Start with a half cup of tea and a half cup of coffee. Take one tablespoon of the tea and mix it in with the coffee. Take one tablespoon of this mixture and mix it back in with the tea. Now decide which cup contains more of its original contents.....

The answer is NIETHER!!!!!

WAIT!! - Before you go all crazy over this not making any sense, let me explain it...... Well, the best way to prove it to you is to give you a demonstration:

Demonstration:

Lets "freeze" the half cup of coffee and tea in our minds. Cut the contents of each up into 50 equal pieces lets say........ Now define a teaspoon as a set number of these pieces. Lets say 5 pieces is a teaspoon. When we take 5 pieces from the tea and put it with the coffee, we have 5 pieces of tea and 100 pieces of coffee in the coffee cup. Mix it up. Now draw out 5 pieces from the mixed cup of 50 coffee and 5 tea pieces and put it in the cup with 45 tea pieces. Since each cup has its original volume of 50 pieces, it is imposible for one to have more of its original contents than the other.

Look at the next column for specific examples of possible outcomes.

Here are some possible outcomes:

(these numbers are the amounts you take from the second cup
of mixed tea and coffee.)

Coffee cup - 45 coffee/5 tea

Tea cup - 45 tea/5 coffee

Coffee cup - 47 coffee/3 tea

Tea cup - 47 tea/3 coffee

In any case, each cup will retain the same amount of its original contents, (relative to each other) after the switch has taken place.

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