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Here's a  fun problem I ran into the other day....I don't even know WHAT the answer is....!!!....but, maybe some creative folks on here would like to propose a solution....heck......there might be even more than one solution...!!!

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In the US, we have these convenience stores known as "7-11's"....well, anyway....

A man goes into a 7-11 and picks up three items and takes them to the clerk.

He asks the clerk, "How much?"

The clerk says, "I multiplied the prices together, and it comes to $7.11." The man says, "Multiplied??....you were supposed to Add those prices together!!" The clerk says, "Doesn't make much difference. Adding them together produces the same total.' The question is......what are the possible prices of the three items??? Have fun....!!! CPhill Jan 22, 2015 ### Best Answer #6 +19603 +15 $$\small{\text{The best solutions: < 0.001 \ difference }}\\\\ \small{\text{ \begin{array}{rcccr} \# & & & & \small{\text{difference in \ }} \\ 1. & \ 4.22 & \ 2.08 & \ 0.81 & 0.000144 \\ 2. & \ 3.21 & \ 3.21 & \ 0.69 & 0.000171 \\ 3. & \ 4.62 & \ 1.35 & \ 1.14 & -0.000180 \\ 4. & \ 3.22 & \ 3.20 & \ 0.69 & 0.000240 \\ 5. & \ 4.37 & \ 1.87 & \ 0.87 & 0.000447 \\ 6. & \ 3.23 & \ 3.19 & \ 0.69 & 0.000447 \\ 7. & \ 3.85 & \ 2.53 & \ 0.73 & -0.000565 \\ 8. & \ 4.25 & \ 2.04 & \ 0.82 & 0.000600 \\ 9. & \ 3.24 & \ 3.18 & \ 0.69 & 0.000792 \end{array} }}$$ (by Computing) heureka Jan 23, 2015 #1 +92751 +5 Thanks Chris, I have added this to the puzzle thread :) Melody Jan 22, 2015 #2 +19603 +10 ......what are the possible prices of the three items : $$\\ \\ 4.62 \qquad \\ 1.35 \qquad \\ 1.14 \\ \dots$$ heureka Jan 23, 2015 #3 +87293 0 Very nice, heureka......can you show us how you arrived at your solution??? CPhill Jan 23, 2015 #4 +26742 +15 Here are a couple of other solutions (though all are approximate, including heureka's, as the products are only accurate to just under 2*10-2 of a cent!):$0.69  $3.21$3.21

$0.81$2.08  $4.22 Solutions obtained by brute force and ignorance! (i.e. running through all possibilities to the nearest cent, from 1cent to$7.11, for two of the items and calculating the third by subtracting the sum from $7.11, then checking to see if the product differs from$7.11 by less than 0.02cents - I didn't do this by hand of course!

I found no solutions when looking for a product that differs from \$7.11 by less than 0.01 cents).

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Alan  Jan 23, 2015
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"Brute Force" and "Ignorance"  are two of my favorite math techniques....in fact, I would feel lost without them....!!!

CPhill  Jan 23, 2015
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$$\small{\text{The best solutions: < 0.001 \ difference }}\\\\ \small{\text{  \begin{array}{rcccr} \# & & & & \small{\text{difference in \ }} \\ 1. & \ 4.22 & \ 2.08 & \ 0.81 & 0.000144 \\ 2. & \ 3.21 & \ 3.21 & \ 0.69 & 0.000171 \\ 3. & \ 4.62 & \ 1.35 & \ 1.14 & -0.000180 \\ 4. & \ 3.22 & \ 3.20 & \ 0.69 & 0.000240 \\ 5. & \ 4.37 & \ 1.87 & \ 0.87 & 0.000447 \\ 6. & \ 3.23 & \ 3.19 & \ 0.69 & 0.000447 \\ 7. & \ 3.85 & \ 2.53 & \ 0.73 & -0.000565 \\ 8. & \ 4.25 & \ 2.04 & \ 0.82 & 0.000600 \\ 9. & \ 3.24 & \ 3.18 & \ 0.69 & 0.000792 \end{array}  }}$$

(by  Computing)

heureka  Jan 23, 2015
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Thanks, heureka.

CPhill  Jan 23, 2015