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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