Tom sent us a nice math trick to demystify. Let's put on our detective hats, click on the image below to see the trick and come back to the Puzzle Marathon to enjoy catching Robin in a fraud and understanding the simple solution.

You pick a two digit number. Let's use letters A and B to define digits in our number. Our number is AB. The value that our number represents is 10 x A + B.

For example, for A=1 and B=5, our number is 10 x 1 + 5 = 15.

Now, Regifting Robin instructs us to subtract both the first and second digit from our number: (10 x A + B) - A - B

Simplifing this we get: 10 x A - A + B - B = 9 x A

For A = 1 we get 9 x 1 = 9

For A = 2 we get 9 x 2 = 18

For A = 3 we get 9 x 3 = 27

Note that continuing with higher As we get all the multiples of 9.

Now we are ready to catch the Regifting Robin in a fraud!

Check Registing Robin's gift table. See what gift is in the cell#9, cell#18, cell#27, and all the other multiples of 9.

What? The same gift???!

No matter what numbers A and B we picked, if we did our math correctly, we get to a cell that is a multiple of 9 and all these cells contain the same gift. No wonder Robin can guess this gift!

Play again and you will see that a different gift is randomly selected but again all the cells that are multiples of 9 have the same gift.

What a fun mass dillusion! Subscribe to our weekly newsletter to get more of such fun tricks by email.

## 3 comments:

Your two-digit number is of the form 10*a + b, where a and b are between 0 and 9.

(10*a + b) - a - b = 9*a. You can see that the table has the same gift for all multiples of 9.

Right. Sometimes it is best to simply countthings; sometimes algebra works best, sometimes we just need to know (somehow) about dodecahedrons or whatever, and sometimes it works best to be iterative (try a few times). Any two digit number, subtract the sum of the digits, and we get some multiple of 9, and then NOTICE that all the 9 multiples have the same breadbox or whatever. Interesting also, to me, that this numerology also works for decimals like 2.8 or 0.00034

Bravo, kj. Tom

A puzzle point for KJ!

Thanks again for sharing this great trick with us, Tom.

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