30 March 2012

Deriving "the number of the Beast" from 123456789

I found this in a Martin Gardner column in a back issue of Isaac Asimov's Science Fiction Magazine.

The "number of the Beast" (666) can be derived in eight different ways by placing + and - signs in the sequence 123456789Only plus and minus signs may be used, and the numbers have to stay in that order.

To me, the most remarkable solution is this one:
+123 +456 +78 +9 
There are five solutions that include the number 678, such as:
-1 +2 -3 +4 -5 +678 -9
And two solutions that use 567 as a component.

I'll defer posting those, to allow those of you who enjoy math puzzles to post your discoveries in the comments.  (btw, there are also five solutions using the descending order 987654321).

Update: Rob from Amersfoort has posted the other answers in the comments.


  1. What is the Mark of the Beast?


    It is the number of a man....

  2. I know that 'the number of the beast' is no longer 666 (which must stink for all of those tattoo folk - not as much as for the homophobic tattoo folk with Judas Priest but I digress). ahem, I discovered a similar formula on my own when I was younger, had more time on my hands and less access to alcohol...
    The sequence was:
    0123+456+78+9 it has an odd 4+3+2+1 to it that I liked a la add ten numbers, get 666 add the 4,3,2,1 and get 10. 10 is much like a boolean ying and yang / good and evil blah blah blah.

  3. +1+2+3+4+567+89 is pretty remarkable too.

    The other ones I found (I love puzzles) are:

    and after some switching of the first 5 components:

    1. Two of your final three are identical, but it's still an impressive accomplishment.

      The only one that eluded you is +1-23-4+5+678+9


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