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COMPUTER PUZZLE 
              By Ted Bik
   This article originally appeared in the ADAM's LEAF, newsletter of the Edmonton (Alberta, Canada) ADAM Users Group and is supplied by the ADAM News Network.
   For all of those who want to become computer analysts there are various problems around to build up expertise in this field. I found one such problem while browsing through an Almanac. It`s a very intriguing puzzle because it is basically simplistic (not in the solution sense) and can be solved with or without the aid of a computer. If you decide to solve it in your mind you will be breaking the egg shell of the puzzle with the delicacy that a diamond cutter cuts a valuable diamond. However if you decide to use a computer to solve the problem then you will be using a technique known as breaking an egg with a hammer. In today's world the hammer and egg approach is becoming more and more frequently used because some problems require volumes of data to be processed in order to obtain a solution. Anyways, the puzzle is to multiply 2 numbers together to find the answer as indicated below:


         X X 7 X Multiplicand 
   
           X 7 X Multiplier 
       ---------
       X X X X X Sub Product 1
  
     X X X 2 X Sub Product 2
  
     8 X 5 X Sub Product 3 
     -----------
     X X X X X X Answer
       
     One rule to remember is that the most significant digit of each number cannot be a zero. As an example take the number given as XXX2X. This is a 5 digit number hence the first X in XXX2X cannot be a zero otherwise this number would be a 4 digit number. 
        
     Now as a hint look at the number 8X5X in the puzzle. Adding this number to XXX2X in the puzzle gives XXXXXX. We know that the first X in XXX2X cannot be a zero, and if it were to be a 2 then the answer XXXXXX would be a 7 digit number (XXXXXXX) instead of a 6 digit number XXXXXX. Hence thus and consequently we know that the first X in XXX2X must be a 1.  Knowing this then it follows that the first X in XXXXXX must be a 9.  That`s it for the hints.

     If you decide to solve this puzzle using the computer, you don`t need the above hint. Instead simply write a small program in SMARTBASIC to multiply all combinations of a 4 digit number with a 3 digit number. When the computer multiplies each number combination check for the following:

     A. Is the tens digit in the Multiplicand a 7.
     B. Is the tens digit in the Multiplier a 7.
     C. Is the first Sub Product a 5 digit number.
     D. Is the second Sub Product a 5 digit number with a 2 in the tens location.  
     E. Is the third Sub Product a 4 digit number with an 8 in the thousands place and a 5 in the tens place.  
     F. If all the above tests are true then add the three Sub Products together, (maintaining the significance of the respective digits in each Sub Product) and check if the Answer is a 6 digit number. 

     If all the above tests prove true then you have the answer. The answer to this puzzle is unique, that is, there is only one answer to this puzzle. One interesting point here is that if you build a program using the above method to find a solution to this puzzle you will find that the time the computer takes to find the solution is twice as long as it would take you to find the solution without the use of the computer.  

     The following is a program that I built to solve the puzzle.  It runs for about 35 minutes before checking all possible combinations. The program however gives more than one answer because I failed to perform one of the checks correctly. Can anybody find the error? 
 
5HOME: d=0: e=0 
10FOR c=1 TO 9 
20 k1=7 
30FOR b=1 TO 9 
40FOR a=1 TO 9 
50 m1$=STR$(c)+STR$(b)+STR$(k1)+STR$(a) 
60 m1=VAL(m1$) 
70FOR e=1 TO 9 
75FOR d=1 TO 9 
77GOSUB 500 
80GOSUB 1000 
85NEXT d 
90NEXT e 
100NEXT a 
110NEXT b 
120NEXT c 
130? 
140? "completed" 
150END 
500 k2=7 
530 m2$=STR$(e)+STR$(k2)+STR$(d) 
540 m2=VAL(m2$) 
550RETURN

    Good Luck, and Have Fun!
                         Ted Bik
 
 
zzle
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