Expressions for Bethe

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Problem Description

Given a set of integers and a target value, construct an expression by inserting arithmetic operators (+, -, x, ) into the set of integers without rearranging them so that the value of the expression equals the target value.  

Background & Techniques

This is a generalized extension of the Expressions100 and  Expressions2002 programs previously posted.  This version will search for solutions for any set of digits and  any integer expression value.   It was prompted by a problem posed by a viewer (Using five 9's, form an expression which equals 10).      

Non-programmers are welcome to read on, but may want to skip to the bottom of this page to download executable version of the program.

Expressions2002 generated all 8 digit  base 3 numbers (00000000 to 22222222) to define operators to be inserted into the 8 slots between the 9 given digits.  Operators there were +, x, and concatenation.   ExpressionsForBethe  extends the concept to base 5 numbers (for the four operators and concatenation) and for a variable number of slots (always one less than the number of input digits).   

I handled the "order of operations" problem in Expressions2002 by introducing a "stack" to hold terms until we know it is OK to evaluate them.   I described the process in some detail there, so i won't repeat it here.  The division operation here needed tests so that we don't try to divide b y zero and to make sure that the quotient is an exact integer (divisor divides the dividend exactly).     

Running/Exploring the Program 

bulletBrowse source extract
bulletDownload source
bulletDownload  executable

Suggestions for Further Explorations

Allow parentheses
Allow user control of allowable set of operators.


Original Date: June 11, 2004 

Modified: May 15, 2018

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