12
$\begingroup$

In the spirit of lightweight prestidigitation, take a break to enjoy a gimmicky digital magic show.

 .'''''''''.---> _________________________              An ordinary 4-digit decimal
 : 3 9 1 8 :--->|                         |             number from the audience,
 '.........'--->|        Binarizer        |             3 9 1 8, is placed in a
           '--->|_________________________|             not-so-mysterious box.
                  | | | | | | | | | | | |
                .'''''''''''''''''''''''''.             12 equivalent digits emerge in a
                : 1 1 1 1 0 1 0 0 1 1 1 0 :             different number system (binary).
                '.........................'
                  | | | | | | | | | | | |               Into another box they go...
                 _V_V_V_V_V_V_V_V_V_V_V_V_
                |                         |----.'''''''.          ...only to reappear
                |         Presto!         |----: j k l :             as an equivalent
                |_________________________|----'.......'             3-digit number  j k l
                                               /   |   \             in another
                                              /    |    \            number system.
                                             / ____V____ \
                                            / |         | \          The middle digit  k
                                           (  | Changeo |  )         becomes an equivalent
                                            \ |_________| /          2-digit number  m n
                                             \    | |    /           in yet another
                                              \   | |   /            number system.
                                              .'''''''''.
                                              : j m n l :            The 4 digits  j m n l
                                              '. . . . .'            together form an
                                                | | | |              amount in yet another
                                            ____V_V_V_V____          number system.
                                           |               |
                                           |  Abracadabra  |         Now for the topper,
                                           |_______________|         after a magical moment
                                                   |                 in one last box, an
                                                   V                 equivalent single
                                                 .'''.               decimal digit  x
                                                 : x :               is presented to a
                                                 '...'               mesmerized audience

The digits 3, 9, 1, 8, j, k, l, m, n and x are all different and none are 0.


Just what do you suppose that mysterious decimal digit x might really be?


Shh, psst...
...it’s not really magic, it’s all done with numbers...
...the original audience number was later spotted in their seat unharmed...
...if this takes more than a few minutes to get solved, I surely will believe in magic.

$\endgroup$
  • $\begingroup$ How can there be ten different digits if none of them are 0? $\endgroup$ – somebody Oct 25 '16 at 4:35
  • $\begingroup$ Good catch on an important clue, @somebody. (The digits are numerical nonetheless, not fingers for instance.) $\endgroup$ – humn Oct 25 '16 at 4:44
14
$\begingroup$

Presto!

convert input to hex.
output (jkl) = f4e

Changeo!

convert middle digit of input to roman numerals.
"4" becomes "iv"; output (jmnl) = five

Abracadabra!

convert text to numeric.
"five" becomes "5"; output (x) = 5

3, 9, 1, 8, j, k, l, m, n and x are all different and none are 0.

3, 9, 1, 8, f, 4, e, i, v, and 5.

$\endgroup$
  • $\begingroup$ +1 for your brilliant and clever solution. But, just for the discussion, can "Abracadabra" be considered a "numeric system" without doubt? (The "Changeo" one is similar but I think there is no problem there) $\endgroup$ – marcoresk Oct 25 '16 at 21:44
  • $\begingroup$ reading carefully, you see binarizer, presto, and changeo all require their input to be converted to an equivalent representation in a different numbering system. binarizer takes decimal digits, treats them as a complete decimal number, and outputs the binary equivalent. presto similarly converts binary input to the identical value in a different system. and changeo, while only operating on a single input digit, likewise converts that digit to its exact equivalent representation in yet another numeric system. $\endgroup$ – Rubio Oct 25 '16 at 21:52
  • 1
    $\begingroup$ Abracadabra is described as taking its four input digits, treating them as an amount in a numeric system (that is to say, those four digits are a representation of a numeric quantity, which is what a numeric system is), and I think we can agree that it can unambiguously be converted to the final equivalent decimal digit in a well defined way, as the problem required. $\endgroup$ – Rubio Oct 25 '16 at 21:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.