Mathemagic!

By Hannah McDowell Friday, September 5, 2014

Welcome to the first edition of Mathemagic! This post will describe some magic tricks you can perform using any objects you can find. I’ve used animals but you could just as easily use coins, playing cards, food, or a selection of different objects you happen to have in your pockets.

The Five Object Trick

Follow along with the trick below:

Image not set

1) Put your finger on any of the animals above.

2) Look at the name of the animal written below. Now you need to move your finger once for each letter in your animal’s name. You must move to the next animal, you can change directions whenever you like and if you get to either end you must change direction. For example: if I choose “Dog” then I put my finger onto the rabbit as I spell “D”, then onto the tiger as I spell “O” and then back onto the rabbit as I spell “G”.

3) Repeat step 2 but with your new animals name.

4) Concentrate on the animal you have now landed on ... it’s not the bee. It isn’t the dog either, we can remove both of those.

Image not set

5) Place your finger on your animal above (if you ended on the rabbit by step 4 then place your finger on the rabbit).

6) Spell out your animal’s name, moving one place for each letter.

7) Move once more, to the nearest animal.

8) Concentrate on your animal...

9) You landed on the Tiger!

I’m not going to tell you how this works... Instead have a go at the simple version below and after you’ve read the solution see if you can work out how the first one works.

1) Place your finger on any animal below.

Image not set

2) Make the same number of movements equal to the number written above the animal.

3) Repeat step 2 but with the number above your new animal.

4) You finger is not on the giraffe, nor the frog.

Image not set

5) Place your finger on your animal above (if you ended on the snake by step 4 then move to the snake).

6) Make the same number of movements equal to the number written above the animal.

7) Now move one more place to the nearest animal.

8) Concentrate on your animal...

9) You landed on the owl!

So... how does this work?

Firstly, with step 2 it is impossible to land on any of the end animals or the centre animal (animal 1, animal 3 or animal 5) after the first go - you must always land on animal 2 or animal 4. This is because some of the numbers are odd, and some are even. Moving from an odd number will always land on an even number, and moving from an even number will always land on an even number. Try it!

Finally with step 7 I ask you to move one more place to the nearest animal – since I’ve eliminated animal 1 and animal 5 and I know you will either be on animal 2 or animal 4 I just need to get you to move one place which will ensure that you will land on animal 3.

Now that you know how it works, can you figure out how the first version of the trick works?

If you want to show this to your friends then you can do it with any five different objects. Place the objects out in a row on a table and point to each one from left to right naming its number position. Then when you eliminate the first and last objects you can remove them from the table and continue as above. I like to do this with five different coins or five objects I’ve borrowed from friends. You could also do this with people by having five people stand in a line and a sixth person can count by pointing at each person one at a time, if you turn your back the whole time then you can name who they have chosen at the end without looking.

You have two options for performing this trick, you could either pretend to be reading your friends mind or pretend to be predicting the future. If you want to pretend to read their minds then do it exactly as above, keeping your back turned and eyes covered you direct them through the process and eventually name the object they have chosen.

If you want to predict the future then you need to write a prediction, you could write the name of the middle object on a piece of paper which you ask your friend to keep in their pocket until later and at the end of the trick you ask them what they chose and get them to remove the prediction from their pocket and read it aloud for anyone watching to hear.

You can find other ways to make predictions depending on the objects you use, for instance with playing cards you could use 4 cards from a blue deck and one card from a red deck but place them all face up on the table, at the end when they turn the cards over they see that they somehow chose the only red card. You could make that even more obvious by writing “You will choose this card” on the back of the red card. Just make sure that you no longer want to use that card for playing games.

Three Object Divination

OK let’s do one more trick. This time you will have three objects on a table and turn your back, your friend will think of one of them and mix up their order. When you turn back you can instantly tell them which object they thought of.

1) Place any three different items onto a table.

2) Number the items from left to right and remember the object in first position.

3) Ask your friend to think of any of the objects they like, they should point at the object so any other people who are watching also know which object they chose.

4) Turn you back and cover your eyes. Ask your friend to switch the two objects they aren’t thinking of. So if they thought of the object at position two then they would switch the objects at position one and three.

5) Now ask them to switch two more objects but to tell you which positions they switch. They can repeat this step as often as they like but they must tell you which positions they switch each time. As they do this you must keep track of position one. So if they say they switch two with three then you do nothing but if they switch one with three then you now think of position three. If they later switch position three with position two then you must think of position two (and so on).

6) When they want to stop switching objects you turn around to face them. Take a look at the position you are currently thinking of. Is the object you remembered in step 2 there? If it is then you know that they chose that object. If it isn’t there then they didn’t choose the object you remembered and they also didn’t choose the object currently in your thought of position – they must be thinking of the only other object remaining.

This trick works because the two objects which are switched at the beginning are the ones they are not thinking of. So if they think of the same object as you then that object will remain in its starting position. However if they think of a different object then the only other object they aren’t thinking of will now be placed into the position you are tracking!

It is important to accurately track your friend’s switches. A handy tip to make the tracking easier is to use your fingers to keep track of the object. If you are currently thinking of position one then touch your thumb to your index finger, position two is your middle finger and position three is your ring finger. That way you cannot forget which position you are thinking of.

Puzzle

Finally I’d like to end with a puzzle, the answer will be posted in the next edition of Mathemagic!

Place between ten and twenty coins on the table. With your eyes closed can you separate the coins into two piles with each pile containing the same number of coins facing heads up? Can you figure out a way to do this without peeking and without feeling each coin to tell what side is up? Join us again next week to learn the answer and for more Mathemagic!

Categories: General | Maths | Magic