We try to keep a tradition of celebrating everyone who wins 10 puzzle points on these ages with a puzzle. This week we are wrapping the Mathmover in our puzzle.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

The Mathmover has been watching the Presidential debates on TV and sipping a tea with milk. More precisely, he started with a full cup of a strong tea to keep himself alert to any surprises on the TV. He drunk one-sixth of the cup during the first two questions and added some milk to fill the cup. By the time Presidential candidates went aggressive he finished one-third of his cup and re-filled it again with milk to keep calm. Later on, when the heat picked up and candidates accused each other of lying, the Mathmover had only half-a-cup of liquid left and topped the cup again with milk to sooth himself toward the bedtime.

The question is whether his wife will have any milk left for her morning-after coffee if they only had a cup of milk left before the debate started.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Image by fionaandneil, distributed under CCL.

## 12 comments:

1/6 + 1/3 + 1/2= 1

Mathmover's wife is drinking black coffee the next morning.

Gurubandhu

Let's assume the "cup" of tea holds an amount of tea equal to the measure of a cup.

Mathmover starts with a cup of tea.

He drinks 1/6, then fills the cup using milk, so he uses 1/6 cup of milk.

He then drinks 1/3 of his cup, and again fills it with milk, using 1/3 cup of milk.

Finally, he drinks 1/2 of his cup and fills it with 1/2 a cup of milk.

He's used 1/6 + 1/3 + 1/2 a cup of milk, or

1/6 + 2/6 + 3/6, or 5/6 a cup. Therefore, his wife will have 1/6 a cup of milk in the morning.

Don't think she'll be all that happy!

Dennis (of Dennis and Katrina)

The wife will have to drink black coffee next morning.

1/6(2 questions) + 1/3(heated argument) = 3/6 or 1/2. Then the final 1/2 toward bedtime makes it a full(1/2 + 1/2) cup of milk that the Mathmover consumed from the start of the debate till bedtime.

1/6 + 1/3 + 1/2 = 1 so, no, there would not be any milk left for the morning.

I can think of 2 ways of doing this problem. The first way is much easier than the second, so we'll start with that.

Method 1

========

Never mind the proportions. All one has to realize is that when 1/6 of the liquid was gone, mathmover filled it up to the top. He used 1/6 of a cup of milk.

He refilled the cup again when he had drunk down 1/3 of the mixture.

His final refill took place when he had 1/2 a cup left.

Answer: The amount of milk used was 1/6 + 1/3 + 1/2 = 1 cup.

Result: His wife has nothing in the morning.

Method Two

==========

Method two is the way I did it until I realized what should be done.

Step One

Refill at 1/6 gone. The cup contains 1/6 milk 5/6 Tea.

Step Two

Mathmover drinks 1/3 of a cup. That 1/3 cup consists of 1/3 of 1/6 = 1/18 milk. He now adds 1/3 cup milk. The total milk content = 1/9 + 1/3 = 4/9 Cup

Step three

Mathmover drinks this mixture until only 1/2 cup remains. What he has drunk is 2/9 of a cup of milk. He fills the cup up with ½ a cup of milk. His total now is 4/9 + 9/18 = 13/18 of cup which he finishes.

At each step, the total amount that he has drunk is

1/18 + 2/9 + 13/18 = 1 cup.

It’s the same 1 cup that we got before, but this is much harder to keep track of.

I hope he wasn’t thinking about this during the debate. On the other hand, thinking about this is far more interesting that some parts of the debate.

His wife will not have any milk left.

He starts by adding 1/6 of the cup, leaving 5/6 remaining, then he adds 1/3 or 2/6 of the cup, leaving 3/6 remaining, he then adds 1/2 or 3/6 of the cup, leaving an empty cup of milk.

The three times that milk was poured, it was in the amounts of 1/6th, 1/3rd and half a cup respectively. The sum of that is precisely one cup, so there won't be any milk left in the morning.

Romney,Obama & cup of tea. The answer to the question as to whether there will be any milk left after "topping" the cup of tea up with milk during certain intervals of the debate, is that there was no milk left. There was 1 cup of milk before the debate started, and at the first interval 1/6 of a cup was used to fill the cup back up to the brim, interval two there was 2/6 of a cup used to fill the cup, and interval 3 there was 3/6 of a cup used to fill the cup back up. 1/6, 2/6, and 3/6 = 6/6 = 1 cup.

Sorry, no milk left for morning coffee! He filled up the cup with 1/6 c. of milk, then 1/3 c., and then 1/2 c.

1/6 + 2/6 + 3/6 = 6/6 = 1cup, which is all they had.

I'm not sure if I'm missing something here. There was full cup of milk before the debate. Mathmover didn't begin pouring milk into his tea until after the debate started.

He poured in 1/6 of a cup, then 1/3 of a cup and finally 1/2 of a cup. This is a total of 1 cup of milk so I am going to say his wife did not have any milk for her morning coffee.

mathmover

.

I don't know if I said this or not: Either way I calculated it, there is no milk left over in the morning. 1 cup mathmover started with and 1 cup he used. Net result, his wife has to go out and replenish the supply (or he does while he's walking the dog -- if there is one).

This is unusual - we all agree here. No milk for the morning. Buy more milk before the next debate and perhaps coffee and some anger-release toy for the election night as it is going to be hot. A puzzle point for everyone.

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