On Friday I posed this puzzle…

John and Joan decide to play several games of cards, with a stake of £1 per game.  After several games John has won three games and Joan has won £3.  How many games did the two of them play?

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

The two of them played nine games.

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.

## 31 comments

1. Canadian Atheist (calm down girls, form an orderly queue) says:

Richard never explains how he arrived at his answer.
This must be very frustrating if you have not worked out the “correct” answer yourself.
Yet again Richard has got the answer wrong – the correct answer is 11 – as the couple also played a couple of games of chess – not for money.

2. Doug says:

John won his 3 games, then Joan won 3, putting them at a draw. Then Joan won another 3, giving her the £3 lead.

(I hope I explained that clearly – I’ve only just woken up…!)

1. Yes, that is how I worked it out. I thought this one was pretty easy and I’m no mathematician.

2. Yup – assuming no draws.

This was less of a puzzle and more of a primary school maths problem.

3. Roland says:

Doug’s explanation will indeed give the clue to Richard’s answer.
All assuming as CA wrote, that they didn’t play other games, or had an unknown number of draws…
I do note that sometimes Richard’s riddles require thinking outside of the box, and sometimes they require rather strict thinking (as this one does)…

4. Kev says:

I got 12. If the stake is £1 per game, not per person, then it’s 50p each. So it would take six wins to be £3 up.

5. ctj says:

six games is a valid solution. the puzzle never says that joan is up by 3, only that she has won 3 pounds. so should could have lost the first 3 games, and then subsequently won 3.

6. Anonymous says:

Ctj in which case she would be back where she started, she needs another three wins to be up three pounds.

1. But, as ctj said, “the puzzle never says that joan is up by 3, only that she has won 3 pounds”.

Personally, my answer was ‘6 or 9, depending on whether Joan won £3 net or only £3’. But I’d say that, going by what’s said, six is the more natural answer. If it’s 9, then Joan has won £6 – albeit she then lost half of it again.

7. Gabby Bollard says:

22/2 = 11. Sorry about the delay in responding

8. Barry Goddard says:

Oh dear, this seems to have generated its usual confusion and wrong answers brought on by a failure to read the question properly.

As I hinted on Friday the answer is six.

To see this take an analogous question: John find three one pound coins in the street while Joan finds three pounds. How much as each got?

We cannot conclude how often Joan picked up, It may have been 300 separated pennies! But if we are asked for the minimum it will be two (a one pound coin and a two pound coin),

Similarly we cannot conclude that John has three pounds more than he started the day with. He may have spent twenty five pounds buying newspapers and cigarettes.

Yet the game conditions in the puzzle are simpler so we can answer. John wins three games so he has played and won three games. Joan wins three pounds so she has played and won three games @ a pound each. Total games played: Three plus Three is SIX unless Bertrand Russell died in vain.

I think the mistake many of the commentators have fallen into is to assume that John and Joan are the only two players at the casino table.

1. More Pedantic and Annoying Than You says:

Oh dear, Barry, like many commentators you have fallen into Richard’s deliberate trap.
Where in the question does it refer to a casino or a table?

2. Barry Goddard says:

@More Pedantic and Annoying Than You

I feel you are being disingenuine. A puzzle gives you all the details you need to FIND the solution. Yet it does not give you all the details that are IN the solution. It is the solver’s task to find those missing details.

As a further example you may be familiar with the type of puzzle that exactly describes a predicament scenario but leaves you to explain it.

Example: A man falls asleep in a very small room. When he wakes up he presses a button and is given a cup of tea.

The solution is that he passed out on an elevator during an evacuation because the building came under a terrorist has attack. When he came too and pressed the alarm button the fireman gave him hot sweet tea as an antidote to shock.

That type of puzzle allows us to hone our minds for the type of puzzle that is set on this blog. Not the number of elements it was necessary to add to create the solution: an elevator, some gas, etc.

I am skilled at solving these types of puzzles and I am happy to help others in doing the same which is why I comment here.

As you say, More Pedantic and Annoying Than You, the people who miss the fine detail miss the open door to enlightenment. Let us neither be that type of person.

3. Less Pedantic and Annoying Than You says:

OK Barry
You win

4. Spammy Fodder says:

Wrong again, Barry. it wouldn’t be much of a puzzle if they had both won 3 games.

The puzzle states that Joan has won 3 pounds, not games, to obscure the fact that she must have actually won 6 games – 3 to win her money back from John and 3 more to win her £3.

To further clarify, if someone wins £3 but also loses £3, they don’t say “I won £3″, they say “I broke even”.

5. Barry Goddard says:

@Spammy Fodder

Thank you for your comment yet I feel you are not being accurate.

If I earn £500 this week and then spend £497 I do not say that at the end of the week I have earned £3.

I earned the £500 irregardless of what I “lost” in spending.

It is the same with the game in the puzzle. If the puzzle was about the ending balances of the players it would have said so. Yet it did not say so. Therefore it was not.

Happy to help you see this more clearly. If you need more help please ask.

6. Spammy Fodder says:

Your analogy is ill-chosen. The puzzle is not concerned with earnings but with wins and losses from a game. We talk about those things differently.

If I go to the races and bet £10 on each of 10 races, win £120 on the first race but lose my money on the others, I don’t go home and say that I won £120 – I say that I won £20.

7. Barry Goddard says:

@Spammy Fodder

If you carefully chose words to mean what YOU want them to mean then you can create any meaning you like in your head. Yet that meaning may not apply in the real world where we have to use words that have common meanings.

I am a professional astrologer so I know the importance of carefully measuring the external reality (star charts) before applying it to subjective conditions (our personal psyches).

You on the other hand seem happy to define “win” and “bet” etc subjectively in order to be right on the internet. That is not a good long term strategy for success and happiness in real life.

8. Borey Saddard says:

Hah, you lost as soon as you called upon pseudo-science to bolster your weak argument. What a pitiful troll you are.

9. Gabby Bollard says:

The mistake (deliberate or other wise) is the vague wording in Mr Wiseman’s question. Does “Joan has won £3” mean that she won £3 in total or as the answer suggests, she was £3 up after a certain number of games. So,assuming the latter, then the “9 games” answer is correct – John won 3 games and Joan won 6 games leaving her £3 up.

And a personal message from me to Richard, stop irritating your followers by posting poorly worded questions or worse still changing the original question over the weekend. It is all becoming a little tedious

1. Lazy T says:

Fart oo sloppy!

2. Nobby Stoppard says:

Do you never wonder if the reason you struggle to understand simple concepts might, just possibly, not be everybody else’s fault?

10. Jerry says:

The problem is much easier to understand if you reword it slightly. If Joan won £3, she won it from John, who obviously lost the £3 to Joan. Then, you can say John won 3 games and also lost £3. That means he won 3 games and lost 6 games, for a total of 9 games played.

11. Pigturion says:

The ambiguity is in the statement “Joan has won £3”. The answers implies this means that she is £3 up on whatever she started with.. Otherwise they could have played 6 games. winning 3 each, meaning that Joan won £3 (but also lost £3).

12. John Cartwright says:

I didn’t try to solve the puzzle this week because I didn’t understand the wording of the question – and I still don’t. What does “with a stake of £1 per game” mean? Does it mean they each pay £1 per game into the central pot? Does it mean the winner takes the £2 from the pot when they win? Does it mean they each pay 50p per game, and the winner gets £1? Does it mean that for each game the loser pays £1 to the winner?

13. John, those aren’t all different: each player paying £1 into a central pot and then the winner taking the £2 is the same as the loser paying £1 to the winner.

In the ‘pot’ case the winner is also paying £1 to themselves, but obviously that doesn’t affect the amount of money transferred between the players.

So your series of questions boils down to: “Does ‘a stake of £1’ mean that a player pays £1 or 50?” The answer is £1.

14. One Eyed Jack says:

Weak sauce. So weak.

15. Anna Lyse says:

I like that with these kind of ambiguous riddles I always find an answer which suits. Sometimes it coincides with Richard’s answer which is also nice.

16. Mis respuestas nunca son acertadas, necesito un curso intensivo en el cual pueda mejorar mas mi capacidad de análisis. Alguien conoce alguno ?

1. El Goddardo says:

Cuando las gaviotas siguen el pesquero, es porque piensan que las sardinas van a ser arrojadas al mar

17. guzzle says:

I thought it through as follows. John has won 3 games which means Joan is 3 quid down. But Joan has 3 quid. So she must have won 6 games. So they played 9 games.