Subj:     Math Prob. - Buying Four Things At 7-11 (S388b)           From: Anonymous Jr on 7/4/2004  A man went into a 7-11 store and chose four items.  The clerk  calculated the total amount which came out to \$7.11. The cust-  omer thought the price was too high so he asked the clerk how  he got that total and the clerk said he multiplied the prices  together to get the total.  The customer asked him to add the prices together and the clerk  came up with the same total - \$7.11.  What were the prices of  the four items the customer bought?  The Right Solution from Jack:  My first approach was to simply solve the system of equations,  which of course gives infinite possibilities.  I thought I'd  be able to use substitution and some "real world" rules to  winnow the results down, but quickly gave up on that path.  The next approach was to turn it into more of a logic problem.  Four values, a.bc, d.ef, etc... with rules about what each  combination gives for its low digit.  I played around with  a.00, d.00, g.hi, j.kl and decided this was going to be too  complicated.  The final approach works nicely.  I'm bothered that there  doesn't seem to be a methodical way to get to the answer,  but maybe I'm just forgetting some concepts.  Anyway, the  solution:  1)  Assume there are no tricks.  That is, the prices are  all positive, and there are no sub-penny prices - not even  2 for 0.99 or some such combination.  2)  Factor the total after adjusting for the number of items.  Since there are 4 items, each with a potential value in the  hundredths position this is 7.11 * 100 * 100 * 100 * 100 =  711000000.  The factors are 79, 5, 5, 5, 5, 5, 5, 3, 3, 2,  2, 2, 2, 2, 2 - the 79, 3, 3 from 711 and the 2s and 5s from  the three remaining 100s.  3)  There aren't that many unique combinations of these  factors into four values, and fewer still that can't be  quickly tossed by inspection.  Trial and error gives:     \$3.16 = 79*2*2     \$1.50 = 2*3*5*5     \$1.25 = 5*5*5     \$1.20 = 5*3*2*2*2     ---------     \$7.11 The items were priced at \$1.20, \$1.25, \$1.50 and \$3.16 which agrees with Jack