On Friday I posted this puzzle.

I have a 100 pound watermelon laying out in the sun. 99% of the watermelon’s weight is water. After a few hours 98% of the watermelon’s weight is water. How much water evaporated?

If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

The answer is 50 pounds – but can you explain why?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. hsw says:

Original watermelon has water:non-water = 99:1
after being in sun it was 98:2 or 49:1 (since the non-water part is unchanged)
so amount of water lost is 99 – 49 = 50

1. Anna Lyse says:

Thanks, well explained.

2. In the first stage the watermelon weighs 100 pounds. Your ratio must also express 100 pounds…and it does.. 99:1. After some time goes by for evaporation the weight of the watermelon is less than 100 pounds, yet your ratio of 98:2 addresses the fruit’s proportions as if it still weighs 100 pounds. I need enlightenment.

3. Anonymous says:

I thought it was 97.02 lbs non-water but it is too long for me to explain. I also dont remember exactly how i got it either.

2. carlosnz says:

Great puzzle. Very counter-intuitive, but then seems obvious in hindsight.

1. One Eyed Jack says:

I found it rather intuitive, but I play a lot of poker so I’m accustomed to calculating odds and percentages on the fly.

I agree that it’s a better puzzle than most of the recent ones.

3. Anne Elk says:

That is quite brilliant. I was not even close. Excellent puzzle. Thank you, Richard.

1. Eddie says:

How come. What was the basic problem stopping you from coming up with the answer?

2. Anne Elk says:

I was faffing about with ratios and all sorts of nonsense.

4. this shows how bamboozled we can become when bombarded with non-intuitive percentage changes – something that pollsters and politicians exploit at our expense all too often.

5. Eddie says:

Must have looked a bit shrivelled up.

6. noname says:

This should help people figuring it out, initially 1% is not water and this 1% equals 1 pound. Later 1 pound is still not water but now this 1 pound is 2%.

1. Garry Boddard says:

Thanks, Sherlock.

2. Gabby Bollard says:

Thanks from me too

7. Annoya Brown says:

Solved it immediately. It is so much easier when Richard posts the answer

8. Barry Goddard says:

This solution makes no sense at all. It does not work for a living breathing being such as a watermelon.

The solution fails to take into account what happens when a real person loses weight. They end up with more skin hanging in crinkly folds. Put simply the volume of the watermelon does not change as much as the surface area and so something has to give.

I do not know what proportion of the one pound was skin as opposed to edible insides but it would have ended up as close to double what it started as.

By failing to take that into account the solution is incomplete.

1. Garry Boddard says:

I think it’s you that’s incomplete, mate.

2. BG:
This is a pure mathematical puzzle, made visual by the description of a watermelon shrinking by evaporation. As you are unable to see beyond the shrivelling remains of the watermelon, you need another visual reference. The simplest, but most boring (to me) puzzle would be an open container of water, allowing free evaporation – the container being 1% of the initial weight.

To make it a little more real-life, try thinking of a 100lb pile of wrapped chocolate bars instead. This is more likely to exist than a giant watermelon and the chocolate and wrappers can be separated cleanly. The wrappers are thrown back into the pile after the chocolates are consumed (just like water evaporating leaves solids behind). The problem becomes “What weight of chocolates need to be eaten so that the percentage of chocolate in the remaining weight drops from 99% to 98%, the other 1% (2% at the end) being wrappers?”.

The answer is the same as for the theoretical watermelon (50lb of chocolate eaten leaving 49lb chocolate and 1lb wrappers), without any need to invent negligible variables to satisfy your inner-troll.

3. One Eyed Jack says:

safc4ever,

Please ignore Barry. He’s just trolling as he’s known to do.

4. Barry Goddard says:

Thank you for your support @safc4ever.

I am glad that someone else understands that our moral astrolabes do not allow us to perform even thought experiments of such a hideous nature on live animals.

Imagine the question had been: “I surgically remove 50% of a kittens body mass. What percentage is now brains if it were 1% to start with?”

The moral outrage would be considerable.

If it is possible to set a problem in a way that does not harm creatures even in the imagination it is our humane duty to do so.

9. Garrd Boddary says:

“This solution makes no sense at all. It does not work for a living breathing being such as a watermelon.”

Fantastic.

1. Lazy T says:

Made me laugh too, but Mars was in Taurus so what can you expect?

10. Garry Boddard, Barry Goddard, Garrd Boddary. I think the three of you should pull yourselves together before someone takes you all for a dry board drag. 😛

1. PeterB says:

Excellent!

2. Gabby Bollard says:

Why have I been excluded?

11. AlistairF says:

W(H2O) = weight of water in watermelon
W(REST) = weight of all non-water items in watermelon

W(H2O) / [ W(H2O) + W(REST) ] = %H2O
To start we are told
W(H2O) + W(REST) = 100
%H2O=0.99
and so we can calculate that
W(H2O) = 99
W(REST)= 1

after evaporation we are told
%H2O = 0.98
and the non-water element remains unchanged
W(REST) = 1

so put these back into the top equation
W(H2O) / [ W(H2O) + 1 ] = 0.98
W(H2O) = 0.98 [ W(H2O) +1 }
W(H2O) = 0.98W(H2O) + 0.98
W(H2O) – 0.98W(H2O) = 0.98
0.02W(H2O)= 0.98
W(H2O) = 0.98 / 0.02 = 49

so evaporated weight of water is 99 – 49 = 50

12. Short answer, with minimal math and no algebra: 1% of original watermelon is not water. That’s 1 pound of “stuff”. After evaporation the same “stuff” is 2% of the total, because the total is now 98% water. 1 pound is 2% of what? 50 pounds. So, it’s lost the other 50 pounds to evaporation.

1. Greg says:

Ken- that’s how I did it. Realised I should be looking for what times 2% = 1. Then just did some trial and error, 90 first then quickly realised I was way off so tried 50.

13. Stephan says:

Another way to calculate it…

x being the water lost… then (99-x)/(100-x)=98/100 which results in x=50 of course

14. Is water the only thing that can evaporate?

15. Bill T. says:

1 ib = .02 x
1/.02 lb = x
50 lb = x

net loss:
100 lb – 50 lb = 50lb

1. Bill T. says:

Some sort of weird spelling “correction going on, 1st equatiuon should read:
1 lb = .02 x

16. Bije z tego bloga naturalnoscia i szczeroscia. Ciesza mnie takie posty, zgadzam sie z kazdym zdaniem.