My magician gives you 3 regular dice
and asks you to do the following, while he is out of the room:
"Roll them, and write in sequence the three results, followed by a 3-digit number representing the hidden sides of the rolled dice.
Once you got the 6–digit number, divide it by 111.
THEN CALL ME."
Then he exits and you roll 1,2,4 and write down 124653, divide by 111 and get 1123.
The magician upon entering the room gets the result and quips within a second 1,2,4.
How did he do it?
(In reply to
Computer results by Charlie)
On the basis of the observed quotients of the division by 111, I tested the hypothesis that that quotient would be (1000*a+100*(b-a)+10*(c-a-(b-a))+7-c), thereby allowing the trick of taking the first digit, adding the first two digits and adding the first three digits, I entered the following into wolfram alpha.
simplify (100000*a+10000*b+1000*c+100*(7-a)+10*(7-b)+7-c)/111 - (1000*a+100*(b-a)+10*(c-a-(b-a))+7-c)
The result was 0 (zero), showing that value was the same as the quotient of the augmented number divided by 111. (The thrown-away last digit is merely 7-c, the complement of the highest dice roll.)
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Posted by Charlie
on 2017-12-12 11:27:25 |
re: Computer results -- proof of sorts
