# Answer to Puzzle #47: Watermelons Drying in The Sun

47. Watermelon is 99% water. I have 100 pounds of watermelon. After a week, drying in the sun, the shrivelled watermelon had only dried down to being 98% water. What is the total weight of the watermelon now?

I don't know about you but I'm guessing it's going to be somewhere in the region of 99lbs plus or minus a little bit that we will calculate. Let's write it out:

Before reading the answer can I interest you in a clue?

Note the phrase

We can see, trivially, that at the beginning of the puzzle the 100lbs of watermelon has 1lb of dry matter and 99lbs of water. So the question, save a little finesse, becomes - what amount of water, when combined with 1lb of dry matter will be 98% water. Take a minute here to think about it. If you still can't get it, it is very possible that you are still being mislead by the deliberate misdirection in the question.

The Dry weight, D

The New Water weight, W

The set up tells us the New Water weight over the New total weight is 0.98 or 98%

W

(X-1)/X = 0.98

X-1 = 0.98X

.02X = 1

X = 50

Which is the answer, 50lbs.

It's interesting how this puzzles manipulates you. When I asked earlier

Note the phrase

*'had only dried down to'*- this is trying to manipulate you in a certain direction. It is clearly trying to suggest the effect is small, which potentially stops you arriving at the answer which, in fact, comes from a large effect.We can see, trivially, that at the beginning of the puzzle the 100lbs of watermelon has 1lb of dry matter and 99lbs of water. So the question, save a little finesse, becomes - what amount of water, when combined with 1lb of dry matter will be 98% water. Take a minute here to think about it. If you still can't get it, it is very possible that you are still being mislead by the deliberate misdirection in the question.

## Explicit Solution

We are to determine X the total mass of melon after the drying.The Dry weight, D

_{W}is 1lb both before and after the drying.The New Water weight, W

_{NW}is clearly X - D_{W}or X - 1The set up tells us the New Water weight over the New total weight is 0.98 or 98%

W

_{NW}/X = 0.98(X-1)/X = 0.98

X-1 = 0.98X

.02X = 1

X = 50

Which is the answer, 50lbs.

It's interesting how this puzzles manipulates you. When I asked earlier

*what amount of water, when combined with 1lb of dry matter will be 98% water*, the answer, 49lbs is obvious. Now. If you got this one without having to work it out congratulations are due.## Assumptions

Assumptions in a puzzle like this are largely to do with the properties of watermelons, density at different temperatures etc. But of course there are no watermelons.© Nigel Coldwell 2004 - – The

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