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.