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## Friday, July 11, 2014

### The Mathematics of 7Eleven®

The chain of 7–11 convenient stores is so called because these family-friendly outlets used to be open from 7:00 a.m. until midnight, but now they're open all the time in the least expected locations: 24/7/365.

Other than munching and gulping at odd hours at 7Eleven stores, these franchise outlets also provide a fertile ground for math educators to come up with some creative math questions to enhance their students' mathematical problem-solving skills. Here are a sample of eleven non-routine elementary and middle-school math questions that may appeal to your students.

 7-eleven.com
1. Number of Convenient Days

In the U.K., 7/11 is abbreviated as 7th November; in the U.S., 7/11 is written as July 11. How many days are there from the U.S. date to the U.K. date?

2. The Recurring 711

What fraction represents the recurring (or repeating) decimal 0.711711711…?

3. The Day of the Week in 711 Days

If 7/11 (July 11 in the United States) is a Friday, which day of the week was 7/11 in 2011? What day of the week will it be 711 days from now?

 Source: Clipart ETC

4. The Acute Angle at 7:11

What is the angle between the minute hand and the hour hand at 7:11?

5. The Likeliest 7/11 Day of the Week

Which day of the week is 7/11 most likely to fall in a 400-year calendrical cycle?

6. Tangram-izing 7/11

Use three sets of the seven-piece Tangram to form the numerals 7 and 11.

7. Number Freaking 7/11

(a) Estimate the average revenue generated by all 7Eleven outlets in the United States every day.

(b) What land or area space is occupied by all 7/11 convenience stores in the world?

8. Are There 711 Digits or More?

How many digits do these indexed numbers have? (a) 711 (b) 7711

9. The 711th Digit Is…

What is the 711th digit of the decimal expansion in the reciprocal of 711?

10. 7Eleven Are Closed …

7Eleven outlets are open 24/7/365. However, on a few occasions some stores had to be closed. Suggest some possible reasons for the closure of these convenient outlets.

11. What Are the Prices in 7-11?

Mr. Yan went inside a 7–11 store and selected four items. When he reached the counter to pay for the goods, the cashier took his calculator, pressed a few buttons and said: "The total price is \$7.11."

Mr. Yan replied, "Are you sure? Do I have to pay \$7.11 because the name of your shop is 7–11?"

The half-embarrassed cashier answered, "Of course not! I've multiplied the prices of these four items and I've just given you the total."

The puzzled Mr. Yan laughed and said, "Why did you multiply these numbers? You'd have added them to get the total price!"

The cashier said, "I'm sorry; I've pressed the wrong button!"

The cashier then repeated all the calculations, by adding the prices of the four items, and to his surprise, the total was still \$7.11.

What are the prices of these four items?

1. 120 days

2. 79/111

3. (i) Monday (ii) Tuesday.

4. 149.5°

8. (ii) 601 digits

9. 9

10. \$3.16, \$1.25, \$1.20, \$1.50.

References
Michalewicz, Z. & Fogel, D. B. (2004). How to solve it: Modern heuristics. New York: Springer-Verlag.
Yan, K. C. (2011). Christmaths—A Singapore math creative problem solving title. Singapore: MathPlus Publishing.

© Yan Kow Cheong, July 11, 2014.

Postscript: This writer isn't sponsored in any way by the 7Eleven brand to write this blog article. However, he won't turn down any cash donations or vouchers, if his e-article has helped challenge and benefit tens of thousands of 7Eleven math fans around the world.