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How and When (Posted on 2009-07-29) Difficulty: 2 of 5
Solve this alphametic, where each of the capital letters in bold denotes a different decimal digit from 0 to 9. None of the numbers can contain any leading zero.

3√(HOW)+ 3√(AND) = 3√(WHEN)

No Solution Yet Submitted by K Sengupta    
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re: Precisely | Comment 15 of 17 |
(In reply to Precisely by ed bottemiller)

The language system or spreadsheet program has to know how much space to allocate for given variables, and so sets the precision of the numbers.  A 32-bit or 64-bit or 16-bit operating system will just gulp given portions of memory faster or slower than another operating system/processor combination.


  ?Limits to QuickBASIC?   ?Names, Strings and Numbers?   ?Contents?   ?Index?
------------------------------------------------------------------------------
Limits to QuickBASIC - Names, Strings, and Numbers
                                       Maximum                 Minimum
Variable name length                   40 characters           1 character
String length                          32,767 characters       0 characters
Integers                               32,767                 -32,768
Long Integers                          2,147,483,647          -2,147,483,648
Single precision numbers (positive)    3.402823 E+38           1.401298 E-45
Single precision numbers (negative)   -1.401298 E-45          -3.402823 E+38
Double precision numbers (positive)
                          Maximum:     1.797693134862315 D+308
                          Minimum:     4.940656458412465 D-324
Double precision (negative)
                          Maximum:    -4.940656458412465 D-324
                          Minimum:    -1.797693134862315 D+308
                

The above comes from the QuickBasic help.                
                
Note the maximum long integer above, 2,147,483,647, for QuickBasic, a DOS product, that ran on 16-bit machines.  This number is 7FFFFFFF in hex, which is 31 bits, and the sign bit makes it 32. It did (and does) this without regard to a 32-bit processor or operating system.

The double-precision floating point numbers are even more precise and indeed also have to allow bits for the exponent portion, as in scientific notation, though binary is used rather than decimal. It requires 8 bytes, or 64 bits. There's a discussion in Wikipedia at http://en.wikipedia.org/wiki/Double_precision_floating-point_format.


  Posted by Charlie on 2009-07-31 14:20:28
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