Earlier today I set you the following puzzle:

Waldemar the Elf has a job to do: he must collect all the Christmas wish lists from children who live in the Sahara Desert. Starting in Timbuktu, he is able to complete the job and return to Timbuktu in 6 days. But he is an elf, which means he is very small. An elf can only carry a maximum of four days worth of elf-food. What is the minimum number of elves Waldemar needs to bring with him to complete the trip?

Clarifications: Waldemar can only travel with other elves. Every elf on the trip must eat a day’s worth of elf food every day. Elf food is not available to buy during the trip, but elves can give each other food. No elf is allowed to leave Timbuktu twice, nor be left stranded in the desert with no food.



First, the solution.

The answer is two elves.



Second, the results.

More than 50,000 of you took part, and you answered in the following way

one elf: 19.o per cent



two elves: 31.3 per cent



three elves: 21.2 per cent



four elves: 11.4 per cent



five elves: 6.2 per cent



six elves: 10.9 per cent



On the plus side, the correct answer was also the most popular answer. Well done!

On the minus side - 31.3 per cent is not very high. Could do better!

The question was originally set in 2010 in a puzzle advent calendar organised by the German Mathematical Society, who told me that about 80 per cent of the schoolchildren (aged 10-16) who entered got the right answer.

I conclude, therefore, that Guardian readers are less smart than German ten-year-olds!

(For those of you who complained that the question was poorly phrased...the German children were asked the same question, and they did a lot better! In your defence, however, I did make the puzzle a bit more tricky than it was for the German children. I let there be six possible answers. In Germany the puzzle only offered only four options to choose from: 0 elves, 1 elf, 2 elves and ‘it’s impossible’.)

Robert Woestenfeld, who set the puzzle, tells me that “children (at least in Germany) are usually brighter than adults when it comes to this sort of out-of-the-box-puzzle.”

The solution, explained:

Waldemar cannot complete the trip on his own, because he will run out of food after four days. So he needs to take at least one companion to carry the extra food.

Let’s say he takes his best friend, Edeltraud. Both elves start off with four days of food supplies. At the end of the first day, the elves have three days of supplies left each.

Now let Edeltraud give Waldemar a day’s supply of food, so Waldemar has four days worth, the maximum he can carry. This means that Edeltraud only has two days worth left.

At the end of the second day, Waldemar will have three days of food left, and Edeltraud has a single day of food. ELF DISASTER ALERT! Waldemar does not have enough food to complete the six day trip, and Edeltraud only has a single day of food left so she must return home or remain stranded in the desert with no food.

So, Waldemar must take at least two companions. Let’s say he takes Edeltraud and Johannes. They all leave Timbuktu with four days of food each.

At the end of the first day, they all have three days of food left. At this point Johannes gives one day of food to Waldemar and one to Edeltraud, leaving Johannes with only one day of food left and his companions with four each. Johannes then returns home.

At the end of the second day, Waldemar and Edeltraud are down to three days of food each. Edeltraud gives one day of food to Waldemar, meaning he has four days worth of food, enough to finish the trip since he has only four days left to go. Edeltraud, down to two days of food, also has enough food to return home and not be stranded.

So, the trip is possible with Waldemar plus two elves.

In fact there is an alternative solution, mentioned by many of you. Waldemar starts off with only Edeltraud, who gives him one day of food as above, leaving him with three days of food left at the end of day two. Waldemar has enough food for five days - but on the sixth day he meets Johannes, who has travelled out from Timbuktu and is waiting for him with his daily ration of food.

Thanks to Robert Woestenfeld who runs the Puzzle Advent Calendar for the German Mathematical Society.

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I post a puzzle here on a Monday every two weeks.

My most recent book is the mathematical adult colouring book Snowflake Seashell Star. (In the US its title is Patterns of the Universe.)

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And if know of any great puzzles that you would like me to set here, get in touch.