Saturday, March 30, 2013

Invisible Dice Trick

Today happens to be the fifth Saturday of the month. Since this doesn't happen very often, I decided to treat you with a little mathematical magic trick.

I first found this trick on the show ScamSchool, where I also found out about Benford's Law. Rather than explaining the trick, you can go watch the video and then I will explain some of the mathematics behind it. Click here for the episode.

This trick requires a little mental math, and also a little algebra to prove to work. It is extremely basic algebra though, so don't get too worried.

With algebra, you denote unknown quantities with a letter. In this example, the unknown quantities are the values of the two dice. We can denote them with a and b. Assume that a is the one that they pulled back.

The instructions were to first multiply a by 2.

a • 2

Next, the spectator had to add five.

2a + 5

Then, the spectator multiplied this quantity by five. This requires the distributive property.

(2a + 5) • 5
(2a) • 5 + (5) • 5
10a + 25

Finally, the person was asked to add the value of the other die, which we called b.

10a + 25 + b
(10a + b) + 25

After rearranging the numbers, you can see the breakdown. If you know that multiplying a number by ten gives you the same number with zero tacked on, you will realize that 10a+b is just a number with a as the first digit and b as the second digit.

So, we have the number that tells us a and b, and this is added to 25 to get the grand total. That is why the performer must subtract 25 to find this number.

I think that this trick is a super simple way to apply mathematics to magic.

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