## Posts tagged ‘7-11’

### Ring Me Up!

When my college roommate contracted crabs, he went to CVS to buy some lice cream. As you can imagine, he didn’t want to announce to the world *what* he was buying or *why*, so he put the box on the counter with a notepad, a bottle of aspirin, a pack of cigarettes, a bag of M&M’s, and a tube of toothpaste — hoping the cream would blend in. The attractive co-ed clerk at the register rang him up without a second look.

As he walked out of the drug store thinking he had gotten away with it, he opened the cigarettes, put one to his lips, and realized he had nothing with which to light it. He returned to the checkout and asked the clerk for a pack of matches.

“Why?” she asked. “If the cream doesn’t work, you gonna burn ’em off?”

Ouch.

My luck with clerks wasn’t much better. At a grocery store, I placed a bar of soap, a container of milk, two boxes of cereal, and a frozen dinner on the check-out counter. The girl at the cash register asked, “Are you single?”

I looked at my items-to-be-purchased. “Pretty obvious, huh?”

“Sure is,” she replied. “You’re a very unattractive man.”

I did, however, have an exceptional experience at a convenience store. This is what happened.

I walked into a 7-11 and took four items to the cash register. The clerk informed me that the register was broken, but she said she could figure the total using her calculator. The clerk then proceeded to

multiplythe prices together and declared that the total was $7.11. Although I knew the prices should have beenadded, not multiplied, I said nothing — as it turns out, the result would have been $7.11 whether the four prices were added or multiplied.There was no sales tax. What was the cost of each item?

As you might have guessed, **that story is completely false**. (The one about me being called ‘unattractive’ is a slight exaggeration. The one about my roommate, sadly, is 100% true.) The truth is that I learned this problem from other instructors when teaching at a gifted summer camp.

It may not be true.** It is, however, one helluva great problem.**

But it has always bothered me that the problem is so difficult. I’ve always wanted a simpler version, so that every student could have an entry point. Today, I spent some time creating a few.

Use the same set-up for each problem below… walk into a store… take some items to check-out counter… multiply instead of add… same total either way. The only difference is the number of items purchased and the total cost.

I’ve tried to rank the problems by level of difficulty. Below, I’ve given some additional explanation — but not the answers… you’ll have to figure them out on your own.

**(trivial)**Two items, $4.00.**(easy)**Two items, $4.50.**(fun)**Two items, $102.01.**(systematic)**Two items, $8.41.**(perfect)**Three items, $6.00.**(tough)**Three items, $6.42.**(rough)**Three items, $5.61.**(insane)**Four items, $6.44.**(the one that started it all)**Four items, $7.11.

*Editor’s Notes*

**trivial** — C’mon, now… even my seven-year-old sons figured this one out!

**easy, fun, systematic** — All of these are systems of two equations in two variables. Should be simple enough for anyone who’s studied basic algebra. All others can use guess-and-check.

**perfect** — Almost as easy as **trivial**, and the name is a hint.

**tough** — But not too tough. Finding one of the prices should be fairly easy. Once you have that, what’s left reduces to a system of equations in two variables.

**rough** — Much tougher than **tough**. None of the prices are easy to find in this one.

**insane** — Gridiculously hard, so how ’bout a hint? Okay. Each item has a unique price under $2.00. If you use brute force and try every possibility, that’s only about 1.5 billion combinations. Shouldn’t take too long to get through all of them…

**the one that started it all** — As tough as **insane**, and not for the faint of heart. But no hint this time. Good luck!

### Problems of Convenience

The candy that my sons received while trick-or-treating all had names with references to various disciplines:

- Baby Ruth – history; named for the daughter of President Grover Cleveland
- Snickers – sports; named after Frank C. Mars’s favorite horse
- 3 Musketeers – literature; named for Athos, Porthos, and Aramis from Alexandre Dumas’s novel
- Milky Way – astronomy; named after the galaxy
- 5th Avenue – geography; named after 5th Avenue in Reading, PA, where the candy bar was originally made

While there was no candy with references to advanced mathematics, several at least had numbers in the names. In addition to 3 Musketeers and 5th Avenue, there were also:

- Zero
- Take 5
- 100 Grand

I visited several local convenience stores to find other candy bars with numbers or math in the name. Sadly, my search yielded no others. Luckily, interesting things always happen when I’m in convenience stores…

A woman walks into a 7-Eleven and takes four items to the cash register. The clerk informs her that the register is broken, but he can figure the total using his calculator. The clerk then proceeds to

multiplythe prices together and declares that the total is $7.11. Although the woman knows the prices should have beenadded, not multiplied, she says nothing — as it turns out, the result would have been $7.11 whether the four prices were added or multiplied.There was no sales tax. What was the cost of each item?

Of course, you may be thinking, “If the four prices were multiplied together, the total would actually be 7.11 dollars^{4}.” And you would be correct. But for the sake of the problem, it’s best not to introduce “quartic dollars” as a unit of measure. I’ll ask that you please suspend disbelief, at least until you’ve solved the problem.

The problem above involves four items, and finding its solution is quite difficult. To reduce the level of difficulty, I wondered if an analogous problem could be created that involves only three items. After an hour of playing with Excel, I was able to create such a problem.

A woman walks into a 6-Sixty and takes three items to the cash register. The clerk informs her that the register is broken, but he can figure the total using his calculator. The clerk then proceeds to

multiplythe prices together and declares that the total is $6.60. Although the woman knows the prices should have beenadded, not multiplied, she says nothing — as it turns out, the result would have been $6.60 whether the three prices were added or multiplied.There was no sales tax. What was the cost of each item?

The problem with only three items is not significantly less difficult than the problem with four items, however, it is helped by the fact that there are two different solutions. Still, I wondered if an analogous problem could be created that involves only two items. Sure enough, one could.

A woman walks into an 8-Forty-One and takes two items to the cash register. The clerk informs her that the register is broken, but he can figure the total using his calculator. The clerk then proceeds to

multiplythe prices together and declares that the total is $8.41. Although the woman knows the prices should have beenadded, not multiplied, she says nothing — as it turns out, the result would have been $8.41 whether the two prices were added or multiplied.There was no sales tax. What was the cost of each item?

This last problem is far less difficult than the other two. Enjoy!

### The Perfect Pack – Redux

Well, glory be!

Two days after lamenting that I had never encountered a perfect pack of M&M’s, and just one day after showing that, on average, only 1 in 64 packs will contain an even number of each color, it finally happened. I bought a pack of M&M’s at the 7-11 (which reminds me of another great problem), and it contained 54 M&M’s in the following distribution of colors:

- Blue – 18
- Brown – 6
- Green – 8
- Yellow – 6
- Orange – 12
- Red – 4

According to the M&M website, the proportion of colors is supposed to be blue, 24%; brown, 13%; green, 16%; yellow, 14%; orange, 20%; and red, 13%. The distribution of colors in the pack that I purchased differs from the expected amounts slightly. But, who cares?

The important point is that there were an even number of each color in the pack! ‘Tis a glorious day!