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He Fooled Penn & Teller but ... (Posted on 2022-12-07) Difficulty: 2 of 5
... he surely can't fool you.

"Penn and Teller: Fool Us" is a TV show on which various magicians present their tricks in front of Penn and Teller, challenging them to explain how they accomplished the trick. They get a reward if they fool Penn and Teller (i.e., they can't explain the trick; their explanations are "coded" so only the magician can understand that they do know the secret behind the trick). Alyson Hannigan, the producer of the show, is also the on-stage presenter of both Penn and Teller and each of the presenting magicians.

This particular magician asked Alyson to use her cell phone calculator app to do the following:

  • Take any month number, 1 - 12.
  • Add any date number (1-31) and press =.
  • Divide by any 4-digit year number and press =.
  • Subtract a local Las Vegas ZIP code, beginning with 891 followed by any two-digit number specified by Teller and press =.
  • Divide by the street address of the hotel theater in which they were performing, stated to be 3700 and press = to get the final answer.

The magician then ran an app on his own cell phone, which amazingly appeared surrounded by floating objects (presumably done by a see-through oversized screen mounted on the cell phone -- he was introduced as a technology geek). Then he pulled out a card by standard magician sleight of hand, and showed it to Penn. It had on it 24.08.

The magician then asked Alyson to recite the first four digits on her answer a digit at a time for added suspense. The first digit was a 2 (preceded by a negative). All four matched the card.

Penn explained that he understood how the objects were made to seem to float around the magician's cell phone, but was mystified as to how the magician knew what the result of the calculation would be, given so many random variables introduced, and so gave the magician the Fool Us award.

But I'm sure you can explain the pre-knowledge of the 24.08.

  Submitted by Charlie    
Rating: 2.0000 (1 votes)
Solution: (Hide)
The maximum that MM x DD can be is 12 * 31 = 372. When divided by the smallest 4-digit year number, 1000, this resullts in .372.

Then when you subtract even just 87100, you get -87099.628. Clearly only the last three digits are majorly affected and only a unit digit is taken from the units position.

When divided by the known (not random) 3700, you get -24.08098....

You might be curious about the opposite end of the choices: month 1, date 1, year 9999, ZIP code 89199.

1*1/9999=.00010001
.00010001-89199=-89198.9999
-89198.9999/3700=-24.08108...

All the variables' differences were pushed far back in the result, beyond the four that were checked.

The most problematic is the zip code. The magician prompted for the 891 portion, and left the remaining two digits to Teller, who was thereby limited to 1 through 10, as he communicated by holding up a number of fingers (as part of his act, he doesn't speak), and the last valid Las Vegas ZIP code ends in 04 anyway. Using the lowest and higest possibilities of each variable:

mo da yyyy  ZIP   unrounded value

 1  1 1000 89100 -24.08108081
 1  1 1000 89110 -24.08378351
 1  1 9999 89100 -24.08108105
 1  1 9999 89110 -24.08378376
 1 31 1000 89100 -24.08107270
 1 31 1000 89110 -24.08377541
 1 31 9999 89100 -24.08108024
 1 31 9999 89110 -24.08378295
12  1 1000 89100 -24.08107784
12  1 1000 89110 -24.08378054
12  1 9999 89100 -24.08108076
12  1 9999 89110 -24.08378346
12 31 1000 89100 -24.08098054
12 31 1000 89110 -24.08368324
12 31 9999 89100 -24.08107103
12 31 9999 89110 -24.08377373


clearvars,clc
for mo=[1 12]
  for da=[1 31]
    for yyyy=[1000 9999]
      for ZIP = [89100 89110]
        unrounded=(mo*da/yyyy-ZIP)/3700;
        fprintf('%2d %2d %4d %5d %10.8f\n',mo,da,yyyy,ZIP,unrounded)
      end
    end
  end
end

Comments: ( You must be logged in to post comments.)
  Subject Author Date
I love this showNatalie Portman2023-03-13 03:06:18
Re:Mira Sherronm2023-02-16 22:07:32
re: Solution -- an asideCharlie2022-12-07 08:31:03
SolutionSolutionLarry2022-12-07 07:41:22
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