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Offline syhprum

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Enigma
« on: 29/01/2009 21:00:04 »
Do any of my fellow geeks ever solve the 'Enigma' competition problems in the NEW SCIENTIST some are horribly difficult to a mathematical ignoramus like me but this week there is a real simple one that can easily be solved by a short brute force BASIC program.

TOM*13 = DALEY, substitute integers for the letters and evaluate DALEY.


 

Offline LeeE

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Enigma
« Reply #1 on: 30/01/2009 13:33:32 »
It shouldn't need a brute-force approach.

DALEY is a five-digit factor of 13, and because none of the digits are duplicated, it must have a minimum value of 10234.

This means that TOM must be greater than 10234/13 = 787.23076

Because TOM not only has no repeated digits but also no digits in common with DALEY it must lie between 789 and 987 and doesn't include the digit '1'

This in turn means that the highest value for DALEY must be 987*13 = 12831, and cannot be in the range 11000-11999 i.e. it must start with either 10 or 12.  Therefore TOM must lie between either 789-845, or 926-987.

I then just knocked up a spreadsheet to display the remaining possible combinations and quickly scanned through the combinations, eliminating further blocks of numbers with duplicated digits, to find that the only solution is:

796*13 = 10348
 

Offline DoctorBeaver

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Enigma
« Reply #2 on: 01/02/2009 14:20:09 »
I did that on my fingers  :P

(OK, I had to use my toes as well)
 

Offline syhprum

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« Reply #3 on: 01/02/2009 15:44:21 »
I first learnt to write BASIC on a Siemens R30 computer a sort of IBM360 clone with a clock speed of 10MHz, I love to to see brute force programs dashing thru in milliseconds on a modern 3GHz machine.
 

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Enigma
« Reply #3 on: 01/02/2009 15:44:21 »

 

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