Truth or Lie
Watch the video below:
If you can't access YouTube, here is a direct link to the video: TruthOrLie.mp4. You can view closed captions by selecting 'CC' in the bottom menu of the video once it is playing.
What do you notice?
Do you have any questions?
Watch it again.
Perhaps some of your questions have been answered. Or you might have thought of new questions.
Using a pack of cards, can you work out how to perform the trick yourself?
Why is this maths and not magic?
This trick, sometimes called The Nine Card Problem, was invented by Jim Steinmeyer.
Could you somehow keep track of the card that was looked at?
Does how you return the cards to the pile when spelling out the card name, matter?
How could you record/share what is going on?
Isaac from North Molton Primary School send in his observations:
So, the woman put three cards on each pile and asked another woman to look at the bottom of any pile. She chose the middle pile. Then the woman doing the trick put the the 10 of diamonds card as the 3rd card. Then she shuffles the deck round and says "Six of diamonds magic". That sentence has exactly 18 letters in it, 18 is also a multiple of 3 so she had shuffled the deck round six times to get to the 10 of diamonds card which was the other lady's card.
Erin from Willowbank School New Zealand wrote:-
You start with nine cards but it has a pattern so it starts off with the pile the person chose and putting it on top of the pile because it has special positions. So if the chosen card was in the middle, the middle would go on top then you do the left pile below it then the right pile underneath the left pile. If the chosen card was in the right pile, the person would choose then do the right one on top then the left one on the bottom and then the middle one. If the chosen card was the left pile you would do the right one below it and then the middle one below that.
Once all nine cards have been put in the right pile order you spell six of diamonds, so basically you go three cards first then add it to the bottom of the pile then two cards then add it to the bottom of the pile then do eight cards then add it to the bottom pile and then spell 'magic', but then you have to flip the first card when you say C then ask the person "IS THIS YOUR CARD".
It takes practice though to perfect it.
Noa and Scarlett from Eden PrimaryӬ School sorted out a sequence they believed was involved:-
The card's position in the pack is always the same number away from the front. The sequence is 3rd, 7th, 5th, 5th. It always starts in the third position.
It also works with any other word followed by 'of' then the name of a type of card. We tried this out with hummus of diamonds, falafel of spades and card of hearts. The trick worked on all three of these words. It only works in words with 3-9 letters. With two letter words, the sequence is 1st, 9th, 1st. With one letter, the sequence is 2nd, 8th, 2nd which is why these don't work.
It can't be any higher in letters than nine because there won't be enough cards.
Eg: Card name: Queen of hearts. Sequence of card placement: 3rd 7th 5th 5th
Card name: king of clubs. Sequence of card placement: 3rd 7th 5th 5th
Card name: ten of spades. Sequence of card placement: 3rd 7th 5th 5th
Card name: Jack of diamonds. Sequence of card placement: 3rd 7th 5th 5th
Alfie, Matilda and Chloe from Crudgington Primary School wrote their conclusions very clearly:
This is not magic it is down to a mathematical sequence.
The chosen card is placed at the bottom of the pile that is then positioned on top of the other two piles, making it always the 3rd card in the deck of cards. This means there will always be six cards below it and two cards are above it.
All the numbers on the cards are no less than three letters long, for example ace is three letters long, 9 is four letters long and 8 is five letters long, this means that the chosen card will always end up second bottom of the pile when counting (see figure 1 below) no matter how many letters the numbers have.
The crucial part is the use of the word 'of' which means the two top cards are then transferred to the bottom of the pile (see figure 2) so that the chosen card will always be in the middle of the pack in position 5 of nine cards - four cards will be above it and four cards will be below it.
As long as the next step (the name of the suits) is greater than 5, of which they all are, then the chosen card will always remain in fifth position.
The word 'magic' contains 5 letters. This means that when you spell out the word 'magic', the c in magic is the 5th letter and your chosen card will always be revealed as it is in the 5th place in the deck.
Sycamore Class from Wensum Junior School wrote about their findings:
We worked out that you need to make sure that the pile your volunteer picks is always put at the top. This makes their card the 3rd one in the pile.
It does not matter which card they pick or if they tell the truth or a lie because the card will always land in a certain place when you place them back in the pile.
For example, if they pick the two of clubs. The first time (two) the card will move to 7th place in the pile. The second time (of) the card will move to the 5th place. The last time (clubs) the card will always move to 5th place. So when you spell out MAGIC, the card will always be when you deal the 'C'.
It doesn't work if you increase the number of cards e.g. if you increase it to four cards per pile, then the card may not be dealt on the first round as it will be 4th in the pile.
Leah and Amelia, also from Eden PrimaryӬ School, went into detail:
Person A - participant
Person B - magician (this trick is not magic)
The first step to this trick is to sort the cards into three piles of three (done by Person B). When Person A chooses a pile, Person B places that pile on top of all the others when collecting the cards. The card Person A has seen is now in the 3rd position because when they pick up the pile their card is at the bottom so when Person B places them face-down it's the third card in the pile.
Person B will now ask Person A to lie or tell the truth about what their card was. It does not affect the outcome of the trick whether Person A lies or tells the truth.
For example: Person A sees the card Ace of Hearts but chooses to lie and say Jack of Clubs. When Person B spells out the word “Jack”, they place “J”, then “A”, then “C” (the third card which is Person A's card). The “K” is the final card to be put down when spelling this word. You place these cards at the bottom of the pile and Person A's card is now at position seven because there are two cards before it (“J” and “A”). It doesn't matter how many cards are placed after it because the smallest amount of letter possible on the first word is three so there are two letters before Person A's card.
The card now moves to the 5th place because when you spell “of” two more cards are placed at the bottom of the pile (neither are Person A's card), so Person A's card moves up two places to the 5th position (7 - 2 = 5).
Next you spell out either “hearts”, “diamonds”, “clubs” or “spades”. There are always going to be four cards in front of Person A's card. This will bring it back to the 5th position. When you spell “magic” the “C” is the fifth letter and Person A's card is in the fifth place. When Person B reveals the letter “C” from the word “magic” they reveal the Ace of Hearts and tell Person A they were lying. This is not a magic trick, this is just a very complicated bit of maths.
Thank you all for the solutions you sent in. Perhaps you could create a different version of this 'trick'? If so, please send it in.
Why do this problem?
Card tricks tap into children's natural curiosity and can provide the motivation for exploring the underlying mathematics in order to unpick how they are done. This particular trick is surprising and intriguing, and will require learners to be resilient as well as methodical.
Possible approach
Play the video without interruption and ask the class what they notice. They may also have questions but rather than share ideas or answer questions at this stage, play the video once more and invite everyone to watch again. Some of the children's questions might have been answered by seeing the clip for a second time, but you could now gather 'noticings' and questions, writing them up
for all to see rather than commenting/answering yourself. It may be that other learners can offer further insight so that some of the questions are answered.
At this point, emphasise that this trick isn't 'magic', it is maths, and ask learners in pairs to try to replicate it. You can leave the video playing on loop so that children can tune in or out at any point. Suggest that children take it in turns in their pairs to do the trick, while the other watches carefully so they work together to try to figure it out.
As they work, look out for those pairs who seem to have found useful strategies, for example a way of recording and/or a way of keeping track of the chosen card. You could facilitate a mini plenary to give time for some pairs to share their ways of working, which may help those who are struggling to make progress.
This could be a simmering activity, so that you leave time for learners to work on the task over a period of a few days, dedicating an area of your 'working wall' to sharing noticings.
A final plenary might involve learners recreating the trick themselves and explaining what they have found out. You might expect them to be able to say something about the position of the chosen card, but not necessarily why this always happens.
Key questions
Could you somehow keep track of the card that was looked at?
Does how you return the cards to the pile when spelling out the card name, matter?
How could you record/share what is going on?
Possible support
You could suggest that learners use a sticky note or something similar to keep track of the chosen card, or turn face up (as opposed to all the other cards being face down) when collecting up the cards for the first time. Knowing that the trick works whether you use the word 'magic' or the word 'maths' might give some a clue.
Possible extension
Invite learners to explore one or more of the following questions:
If you had more than nine cards, what would happen?
Can you explain why the trick always works?