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And equality for all.... (Posted on 2007-12-11) Difficulty: 4 of 5
Find the largest number, a single string of only digits - without radix or exponent, that can be equated to a mathematical expression that uses no variables and where each and every digit, 0 to 9, is used but once in the equation. Provide the equation.
Mathematical symbols and functions are permitted, yet limit each to less than the arbitrary number of ten.
If limited to digits 0 to 5, a possible answer, for example, could be:
5!/(4 - 3) = 120.

  Submitted by Dej Mar    
Rating: 2.5000 (2 votes)
Solution: (Hide)

This submission was more a challenge than a puzzle, though puzzling it may have been.
Under the requirements proposed, ideally the equation would be of the form F(x) = n, where F(x) was the combination of various math functions using the single smallest digit, i.e., 0 to seed the function and n equalling the largest number possible with the remaining digits, i.e., 987654321.
Using various math functions the result might possibly be attained. For instance, examine the following equation:

|_cosh(|_(cosh(]tan(0!)[)_|)_|! - 4 - 1 = 3628795

such that |_x_| is the floor function and ]x[ is the ceiling function.
As can be seen, with a single 0 a much larger number was acquired.

When I had submitted the challenge, I had limited myself to only a few functions. As such, the largest candidate I've found was:

p8# + 6$ * 1 = 9734250

  • p8# (or 8#, the primorial of 8; 1st definition) = 9699690;
  • 6$ (the superfactorial of 6) = 34560

As to the largest number for the digits 0 to 5, one candidate might be:

(5!! - 4)# = 2310

  • 5!! (the double factorial of 5) = 15;
  • 11# (the primorial of 11; 2nd definition) = 2310

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionimproved ... a littleAdy TZIDON2007-12-15 12:29:03
re(2): 6 digits (3 x10^6)Leming2007-12-12 22:49:57
Questionre: 6 digits (3 x10^6)Ady TZIDON2007-12-12 18:41:51
Solutionre: 6 digits (3 x10^6)Ady TZIDON2007-12-12 18:38:11
Solution6 digits (3 x10^6)Leming2007-12-12 18:18:15
Solutionre(2): three MOREAdy TZIDON2007-12-12 17:16:53
Some Thoughtsre: three MORELeming2007-12-12 16:06:47
Solutionthree MOREAdy TZIDON2007-12-12 15:44:02
SolutionONE OF MANY STUPID SOLUTIONSAdy TZIDON2007-12-12 15:34:35
SolutionIt's just that easy!Jyqm2007-12-11 19:55:11
SolutionA little less, but no operations on the right side.Leming2007-12-11 16:33:50
Hints/Tipsre: another - not quite right - answerDej Mar2007-12-11 12:44:02
another - not quite right - answerLeming2007-12-11 11:27:00
So close - but off by one number.Leming2007-12-11 11:18:13
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