Brain Teasers – The Answers

A couple of days ago I posted several brain teasers here (and introduced the brilliant brain teaser book, Enigma), and left it up to you, my awesome readers, to try and solve them. Impressively, within 24 hours all of them were answered by various people in the comments, so now I shall reveal the answers for you all (but feel free to go back and try them first, of course, if you haven’t yet done so).

I’ll repeat each puzzle, then reveal the answer in italics afterwards.

Puzzle One:

At a tournament, there is a tie between two knights. To decide between them, the king says to them: “See the tower rising over the horizon? The one whose horse arrives last at the tower will win the tournament.” With these words, both knights run to the stables, mount a horse and head straight towards the tower at a great gallop! How can we explain the knights’ illogical behaviour?

Answer:

They mounted each other’s horses! This puzzle tricks people more when told verbally, instead of being written down, as people tend not to notice the clues in the wording.

Puzzle Two:

Godfrey of Bouillon has five children. Half are daughters. How can this be explained?

Answer:

They’re all daughters. Just because half are daughters, doesn’t mean the other half aren’t daughters. But I am aware how much this answer annoys some people. Still, I think it’s clever.

Puzzle Three:

During a knights’ tournament, a man and his son are two of the candidates in the lists. The father is hit by a lance and he dies on the spot. His son, also wounded, is carried into a tent. The doctor in charge of examining him leans over the stretcher and exclaims “My God! It’s my son!” How is this possible?

Answer:

The doctor is his mother.

Puzzle Four:

Three travellers stop over at an inn, where they hire a room for 30 pennies a night. They each put in 10 pennies. Because the innkeeper likes them, he lowers the price to 25 pennies and gives them back 5 pennies. But there are three of them, so they take 1 penny each and leave the 2 pennies left over as a tip. So each of them has paid 9 pennies (3 x 9 = 27) and the innkeeper gets 2 pennies back. But 27 + 2 = 29. Where has the thirtieth penny gone?

Answer:

This one is a trick question – the thirtieth penny hasn’t gone anywhere. Each of them has paid 9 pennies, but the 27 pennies includes the 25 the innkeeper charged and the 2 they gave back, and the other three the travellers took. The question is worded to make you doubt the mathematics, but everything was fine all along. Interestingly, this one has stumped many adults for days, yet just today I asked one of my year 8 students this one (he’s 13, 14 years old), and he got it almost instantaneously, which shows how different age groups can think so differently.

Puzzle Five:

How can you make 24, using each of the numbers 5, 5, 5 and 1 once? The only operations allowed are addition, subtraction, multiplication and division (but you can use brackets, too, to play around with the order of the operations).

Answer:

Only one person got this one, but I will admit this was very challenging. Displayed as a single line equation, it looks something like this:
[5-(1/5)] x 5 = 24
or in steps, looks like this:
1/5 = 0.2
5 – 0.2 = 4.8
4.8 x 5 = 24
Generally I found my students with this one have jumped straight into multiplying 5 by 5, and subtracting 1, only to then realise they have the answer but also have to use another 5. To divide the 1 by the 5 tends to go against most people’s natural mathematical reasoning.

I hope you all had fun with these – I know I did, and I enjoyed seeing the ways in which people answered. I think I may have to do some more posts like this down the track, yes?

12 thoughts on “Brain Teasers – The Answers

  1. yes – they were fun but I didn’t even try the number ones – the daughter one puzzled me and then it was doh and a slapped forehead moment – 🙂

  2. Bahh.. math is NOT my strong side obviously.. haha but I did work out that the doctor who exclaims “this is my son” is in fact his mother :p and the “five children” one I also figured out but you already knew that. I did not figure out the knights and horses one… but when I read the answers I really felt “doh” haha 😛 Great posts!

    • Hahaha, I think math isn’t a strong side for most people, by the seems of things! Good work getting the mother one though, and yes that was good watching you unravel the daughter one the other day when I told you that one, hehehe 🙂 The knights and horses one is quite tricky, as the answer is hiding in the question really. But I wouldn’t feel too “doh”…these questions are designed that way on purpose 😉

  3. I knew the answers to puzzle 3 and 4. In fact, puzzle 4 has been one of my favorites for years. It does stump a lot of people. The others stumped me and yes, I am annoyed at the answer to puzzle 2. Half of 5 daughters is 2 1/2 daughters!

    • I agree, 4 is a great one, and one I’ve memorised now so I can challenge more people with it. As for puzzle 2, yep, half is 2 and a half daughters, and the other half is the other 2 and a half daughters! Technically it works fine 😛

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