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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.

See The Solution Submitted by Charlie    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 5
Consider the possible extreme values that the calculator could show at the end, and go step by step.

Month + Day:  (2, 43)
(divide by) 4-digit year: (1000,9999)
(subtract) zip code:   (89100,89199)
(divide by) address:    (3700,3700)

smallest:  (2/9999 - 89199)/3700 = -24.10783778377838
largest:   (43/1000 - 89100)/3700 = -24.081069459459457

oops, the smallest (largest absolute value, since it is negative) yields 2410 instead of 2408.  But, aha! All is not lost, because Teller gets to specify the last 2 digits of the zip code.  So varying n in 89100 + n shows that as long as n is 33 or less, the first four digits will be 2408


n  result
0 -24.08108102702162
1 -24.081351297291892
2 -24.081621567562163
...
...
32 -24.08972967567027
33 -24.08999994594054
34 -24.09027021621081
35 -24.09054048648108
...
...
98 -24.10756751350811
99 -24.10783778377838

But I have no idea how his cell phone appeared to be surrounded by floating objects.

  Posted by Larry on 2022-12-07 07:41:22
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