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PUZZLET 86 - THE SOLUTION

' Puzzlet #086 ' The sides of a box are all an exact nr ' of cm (no decimal points), each having ' 2 digits. The height, width, and depth ' are  all different.  The volume is ten ' times the surface area,  which in turn ' is  exactly 31.5 times the sum of  the ' lengths of all twelve edges. ' What are the dimensions of the box? ' By Dave Ellis. declare PrintIt() def height, width, depth: int def volume, area, edgeLength: int openconsole print "Searching ...": print for height = 10 to 97     for depth = height + 1 to 98         for width = depth + 1 to 99             volume = height*width*depth             area = 2*(height*width + height*depth + width*depth)             if volume = 10 * area                 edgeLength = 4 * (height + width + depth)                 if area = 31.5*edgeLength                     PrintIt()                 endif             endif         next width     next depth next height print: print "No more!" print: print "Press any key to exit ..." do: until inkey$ <> "" closeconsole end    sub PrintIt 'pretty printer print "Height:     ", height print "Width:      ", width print "Depth:      ", depth print "Area:       ", area print "Volume:     ", volume print "EdgeLength: ", edgeLength return

PROGRAM NOTES Each of the box's parameters are given a self-evident variable name: height, width, depth, area, volume, and edgeLength. Using three nested for-next loops, all possible combinations of three different two digit integers are generated as values for height, width, and depth. For each combination, the volume is calculated from the line:  volume = height*width*depth, then the surface area from the line:  area = 2*(height*width + height*depth + width*depth). Having obtained the box's area and volume, we can go on to ask the question "Is the volume numerically 10 times the area?" If the answer is yes, we ask a second, final question: "Is the area 31.5 times the combined edge lengths?" If this answer is also yes, we've found the solution, and the current variable values are printed out by the subroutine PrintIt().

When you run the program, you'll see the following on your screen. As required, height, width and depth are all different 2-digit integers. The volume is 10 times the area and the area is 31.5 times the edge length.

Searching ... Height:     42 Width:      84 Depth:      70 Area:       24696 Volume:     246960 EdgeLength: 784 No more! Press a key ...

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