Science, Maths & Technology
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Updated Tuesday, 24th March 2009

In this video it seems as though your mind had been read – but how is that possible? Discover the magic of maths

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Transcript

## The explanation

Well we’re not big believers in mind reading – this is just a party trick that is based on some simple counting patterns.

So how does it work?

#### 1) First instruction

The first instruction was "pick a number between 5 and 15", then step the number in an anti-clockwise direction. By following this, you can only land on either 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12. It is not possible to land on 1, 2, or 3 at this point.

Starting point

#### 2) Second instruction

You’re then asked to move in the opposite direction from the place you have just landed on. For example, if you’re on 3 (then your chosen number must have been 5), so counting 5 steps in an anticlockwise direction from 3 you end up on 10:

2, 1, 12, 11, 10

Now move in the opposite direction

If you’re on 4, then you chose 6, so counting in an anticlockwise direction from 4 – you’d now be on 10:

3, 2, 1, 12, 11, 10

If you’re on 5, then your chosen number is 7 – so you would now be on 10:

4, 3, 2, 1, 12, 11, 10

If you’re on 6, then your chosen number is 8 – so you would now be on 10:

5, 4, 3, 2, 1, 12, 11,10

If you’re on 7, then your chosen number is 9 – so you would now be on 10:

6, 5, 4, 3, 2, 1, 12, 11, 10

If you’re on 8, then your chosen number is 10 – so you would now be on 10:

7, 6, 5, 4, 3, 2, 1, 12, 11, 10

If you’re on 9, then your chosen number is 11 – so you would now be on 10:

8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10

If you’re on 10, then your chosen number is 12 – so you would now be on 10:

9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10

If you’re on 11, then your chosen number is 13 – so you would now be on 10:

10,9,8,7,6,5,4, 3,2,1,11,10

If you’re on 12, then your chosen number is 14 – so you would now be on 10:

11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10

If you’re on 1, then your chosen number is 15 – so you would now be on 10:

12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10

So you can probably see the pattern, whatever number you chose – you will be on 10 by the time you have finished stepping.

We then take 12, 8, 6, off the circle.

Numbers 12, 8 & 6 are removed

#### 3) Third instruction

You are then asked to count four steps in either direction.

If we lay out the number line with 10 in the middle, and count four steps in either direction you get the following:

3 ← 2 ← 1 ← 11 ← 10 → 9 → 7 → 5 → 3

Heading in either direction – counting four steps – you will always land on 3.

So there’s no magic here. To understand the problem, you don’t need complex arithmetic – just an interest in problem solving, rules, patterns and structures. In fact, lots of mathematics is like this.