# Aisle 16 Homework Answers

For nearly two decades, the leadership team of Steelcase, the office furniture manufacturer, was located on one of the top floors of the global corporate headquarters in Grand Rapids, Michigan, overlooking the prairie surrounding its campus. In 2014, after Jim Keane was promoted from COO to CEO, he decided to move the leadership team across campus to what the company calls the Learning and Innovation Center, the main crossroads through which employees frequently pass. The new office space on the ground floor is now buzzing with interactions between leaders, employee teams and customers throughout the day.”

“I loved my old office and old space. Loved it. Loved it. Loved it,” says Keane, “[But] the way my team [now] flanks the core aisle, the majority of office activity funnels down that aisle, and we get to witness it all. I’m not going to learn anything if I just keep working with something that is very comfortable for me.”

The leadership team’s move to the ground floor is part of a broader effort that Keane is now executing to align the company with his personal philosophy about work and how to create value, forged early in his life.

#### Unlocking Human Promise

Until high school, Keane says that “things came pretty easily” for him and he was “coasting” and not really applying himself. In ninth grade, his math teacher called him out on it. “He knew I could use a little kick in the butt,” he says.

One day, the teacher was frustrated with Keane for not doing his homework, so he called on him to answer the first question and he didn’t know the answer. He called on Jim to answer the second question and he didn’t know the answer. Keane was uncomfortable but, in the end, inspired.

“By pushing me, this teacher showed me what I was capable of doing. He awoke something inside me.” Keane credits this moment for sparking something that has since evolved into the philosophy that still drives him to this day, and is at the root of his leadership at Steelcase.

Moving himself and the leadership team to the center of action has made it very difficult for the team to coast because the executives are constantly provoked and held accountable by employees and customers. This has created a new dynamic within the leaders and the company as a whole.

The new space puts the senior leaders in a more accessible position, literally, with everyone who comes through headquarters. It’s creating more unplanned interactions between the leadership team, employees and customers. The senior leadership team now has a better pulse on how things are going. It has provoked his team to take on new challenges while giving up control at the same time.

Keane now bumps into at least two customer groups per day on top of the meetings he has formally scheduled. He is able to hear firsthand about the work Steelcase is doing for them. Keane admits the feedback isn’t always positive, “but it is always constructive.” These are exactly the challenges that inspire everyone in the company to get better.

Keane is also building a culture of provoking clients with new ideas that they might find uncomfortable. He’s quick to add, “Clients like the challenge. If they are going to spend a lot of money on building or renovation, they don’t want us to just be polite. We push them see what is possible.”

#### Fostering Excellence

“There are all these companies out there trying to promote diversity of thought, but once they hire those people they want the employees to be exactly the same.” Keane sees this as symbolic of the trend toward “cubicle farms” where each employee’s workstation looks identical. “They have squashed human spirit, instead of inspiring it.”

By contrast, at Steelcase, employees have the freedom to personalize the design of their workplaces. They can step away from open office space to work in quiet rooms, take breaks by walking outside on campus or work in a variety of settings.

While Keane likes to give his employees autonomy, he is also competitive when it comes to challenging his team. He regularly asks, “How can you be better today than you were yesterday?” He pushes himself and others — like his math teacher pushed him — to see what they are capable of achieving. He believes “competition between organizations and within ourselves is a good thing. It is the force that unlocks human promise.”

#### A Purposeful Workspace

On the new ground floor offices at Steelcase, work has changed radically for Keane and his leadership team. The changed environment, from his point of view, has directly impacted their level of fulfillment they experience in their jobs.

Today, Keane’s days are filled with the constant stream of interactions with people who pass through the leadership space, which he refers to as “the river.” He never would have bumped into as many employees or customers in his old office, tucked away at the top of a building and away from the rest of the organization. He connects with employees he hasn’t seen in months, if not years. “My days begin and end with people now.”

What drives Keane is very similar to what drove Steve Jobs. Jobs had a metaphor he would share that nicely sums up his philosophy, and the philosophy that is at the core of Keane’s purpose. Jobs described a rock tumbler. Remember those spinning cylinder cages you had as a kid? You put some generic rocks from the garden in them and let them tumble overnight. In the morning they emerged as shiny, beautiful stones? Frequent collisions between people have the same impact. They soften one’s edges and expose the hidden beauty and potential.

#### A Parallel Purpose Journey

Relationships are key to experiencing purpose in our jobs everyday, as our research at Imperative has shown. And, Steelcase’s experience shows relationships are forged not just through the intensity of our interactions but also through the frequency of interaction. They encompass all our planned meetings as well as the creative collisions sparked by unplanned encounters throughout our workday.

For leaders, the journey to personal purpose often coincides with a parallel journey for their organizations. As Steelcase has evolved, Keane has come to understand that doing good work is about more than working for a good company or tackling interesting challenges, as he used to believe early on his career. Instead, it’s about having a positive impact on those you work with, and about helping your employees grow. He now leads his team with these expectations so they in turn can help their customers rethink how they work.

*This article is part of a series of articles by Aaron Hurst exploring how leaders find purpose and meaning in their jobs. Last fall, Hurst’s company, Imperative, released a global survey of the role of purpose at work, in partnership with LinkedIn Talent Solutions, which found that those who are intrinsically motivated to find purpose in their jobs consistently outperform their colleagues and experience greater levels of job satisfaction and well-being, regardless of country, gender, or ethnicity. They are also 50% more likely to be leaders. This series will profile those leaders, and how they connect with what’s meaningful to them in their role and the organizations they lead.*

*Aaron Hurst is a globally recognized entrepreneur and authority on social innovation. He is the CEO of Imperative and founder of the Taproot Foundation. His book,*The Purpose Economy*, is now available as a paperback.*

## Homework

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[Chapter 1 & 2][Tree diagram for counting combinations]

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** **

**Answers to Homework Problems**

**Warning: **You should only use these answers to check the correctness of your work

and you need to show all steps for any credit.

*Chapter I, Problem Set**A*

*Chapter I, Problem Set*

*A*

**1. WORM JOURNEY**

* 10 days*

* *

**2. THE UPS AND DOWNS OF SHOPPING**

** ***13 floors*

* *

**3. FOLLOW THE BOUNCING BALL**

** ***460 feet*

* *

**4. FLOOR TILES**

** ***320 tiles*

* *

**5. COUNTING ON NINJA TURTLES **

** ***22**turtles*

* *

**7. RACE**

** ***Ursula, Alma (3 m behind), Cathy (3 m behind), Lani (2 m behind), Isabel (2 m behind), and Betty (2 m behind)*

* *

**8. ****A WHOLE LOTTA SHAKIN' GOIN' ON!**

** ***15 handshakes*

* **Chapter 2, Problem Set A*

*Chapter 2, Problem Set A*

* *

**1. CARDS AND COMICS**

** Cards @ $1.20 ****Comics @ ****$.60**

** ***5 0*

*4 2*

*3 4*

*2 6*

*1 8*

*0 10*

* *

**2. FREE CONCERT TICKETS**

** **

*A = Alexis, etc.*

*ABCD BACD CABD DABC*

*ABDC BADC CADB DACB*

*ACBD BCAD CBAD DBAC*

*ACDB BCDA CBDA DBCA*

*ADBC BDAC CDAB DCAB*

*ADCB BDCA CDBA DCBA*

* *

**3. IT SURE IS TOUGH TO GET AN APARTMENT THESE DAYS**

** **

*In the ninth month Plan A costs more ($640 per month vs. $620 per month for Plan B). But for the whole year plan B costs more ($6990 total vs. $6780 for Plan A).*

* *

**4. STORAGE SHEDS**

8 ft x 8 ft 10 ft x 10 ft 12ft x l2ft 15 ft x 15 ft

8 ft x 10 ft 10 ft x 12 ft 12ft x 15 ft

8 ft x 12 ft 10 ft x 15 ft

8 ft x 15 ft

* *

**5. MAKING CHANGE**

** **

*10 ways*

* *

**7. **

**KYLE CRAVES CANDY**

There are 10 ways

** **

**Five Ten Fifteen Total **

* 8 0 0 40*

* 6 1 0 40*

* 5 0 1 40*

* 4 2 0 40*

* 3 1 1 40*

* 2 3 0 40*

* 2 0 2 40*

* 1 2 1 40*

* 0 4 0 40*

* 0 1 2 40*

*Chapter 3, Problem Set**A*

* *

* *

*3***. EGGS IN A BASKET**

** **

*119*

*4***. DARTBOARD**

** **

*23, 58, 31, 6, 15*

* *

*5***. FIND THE NUMBER**

** **

* Answer: abcd is 2178*

*6.*** a. GIRLS + GIRLS = SILLY **

*Two possible answers: *

*G = 3, I = 0, L = 9, R = 4, S = 6, Y = 2 OR G = 1, I = 9, L = 0, R = 5, S = 3, Y = 6 *

* ***b. GOOD + DOG = FANGS **

*A = 0, D = 8, F = 1, G = 9, N = 2, 0 = 4, S = 7*

* *

*7.*** SEND + MORE = MONEY**

* 9567 + 1085 = 10652*

* *

*8***. THE THREE SQUARES**

* Chris is 19, Phyllis is 23, Bob is 28.*

*9*. KNIGHTS AND KNAVES

** **

* There is only one knight.*

* *

* *

*Chapter 3, Problem Set B*

*1. ***THE SIDEWALK AROUND THE GARDEN**

** **

* 172 feet*

* *

*2. ***A NUMBER OF OPTIONS**

** **

* 24 ways*

* *

*3***. GOOD DIRECTIONS?**

** **

*Go 2 blocks east and one block south. (two more possible answers)*

* *

*4***. HIGH SCORERS**

** **

*Heather: 25;**Sara: 23*; *Martina: 19; Donna: 17; Kellene: 11*

* *

*5***. WAYS TO SCORE**

** **

* 14 ways*

* *

* *

*Chapter 4, Problem *Set *A*

* *

*1. ***SCHEDULES**

* a. Jill's schedule b. Tom's schedule*

* 1 Band I PE*

* 2 PE 2 Math*

* 3 Science 3 Drama*

* 4 Math 4 Science*

* 5 Lunch 5 Lunch*

* 6 English 6 English*

* 7 History 7 Typing*

*c. Leanne's schedule is impossible as she has to take both Math and PE during second period and has no class to take during seventh period.*

*d. Mea's schedule has many possibilities.*

*e. Part I: Jose's first schedule looks like this*

* 1 PE*

* 2 Math*

* 3 Drama*

* 4 Science*

* 5 Lunch*

* 6 English*

* 7 History*

* Part 2: Because first period PE is closed, there is no way for Jose's schedule to work. He won't be able to take Drama because he will have to take Science third period to make his schedule work. So he must pick another elective, either Band or Typing.*

* *

* *

* *

** ***Part 3: Now with the new sixth period science class, Jose's schedule will work.*

* 1 English*

* 2 Math (Note: Math and PE can be switched.)*

* 3 Drama*

* 4 Lunch*

* 5 PL*

* 6 Science*

* 7 History*

* *

** **

*2. ***THE FISHING TRIP**

** **

*Sally first, Larry second, Woody third, Marta fourth*

* *

*3. ***CABINET MEMBERS**

* Georgianne, President; Norma, Vice President; Inez, secretary of state; Paula, secretary of education; Colleen, secretary of treasury*

* *

*5. ***MUSIC PREFERENCES**

* Jack Mullin, country western; Mike Hardaway, rock; Adele Higgins, Jazz; Edna Richmond, classical*

* *

*6. ***SUSPECTS**

* Connie Wilde, purple hair: Morgan Theeves, scar; *

*Dana, tall and blonde;*

Cary Fleece, birthmark

Cary Fleece, birthmark

* *

*Chapter 4, Problem Set B*

*1. ***PHONE NUMBER**

* 492-2804*

* *

*3. ***SPORTING EVENTS**

* Ed, baseball, Monday*

* Judy frisbee, Tuesday*

* Mama, golf Thursday*

* Lisa, soccer, Friday*

* *

*4. ***THE BILLBOARD**

* 7 lines*

* *

*Chapter 5, Problem Set**A*

* *

*1. ***SEQUENCE PATTERNS**

** **

* a. 2, 5, 10, 17, 26, 37, *

*50**Add next odd number. Or, each term is 1 more than a perfect square.*

* *

* b. 64, 32, 16, 8, 4, 2, 1, 1/2*

*Divide by 2. Or, each term is a descending power of 2.*

* *

* c. 5, 10, 9, 18, **17, **34, 33, 66, 65, 130*

*Multiply by 2 and then subtract 1.*

* *

* d. 1, 3, 7, 13, 21, 31, 43, 57*

*Add the next even number.*

* *

* e. 2, 3, 5, 9, 17,33, 65*

*Add the next power of 2. Or, 2, 3, 5, 9, 16, 27, 43*.

*The difference of the differences increases by*

*1.*

*There are probably other answers.*

* *

* f **1, **5, 13, 26, 45, 71, 105, 148, 201*

*Starting with 4, the difference of the differences increases by 1.*

* *

* g. 1, 2, 6, 24, 120, **720, **5040, 40320, 362880*

*Multiply by the next higher number. Or, each term is just n! (n factorial).*

* h. 1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177*

*Add the two previous terms and then add 1.*

*2. ***AIR SHOW**

* 400*

*The pattern is the square of the number of rows.*

* *

*3. ***RECTANGULAR DOTS**

** **

* 34 x 35 = 1190*

* *

*4. ***PENTAGONAL NUMBERS**

** **

* 425*

*Add together a triangular number and a square number. The triangular number has one fewer dots per side than the square number.*

* *

*5. ***LAST DIGIT**

** **

* 2 ^{57 }ends in 2. The pattern goes 2,4,8,6,*

* *

*8. ***BEES**

** **

* 231*

*This is a Fibonacci sequence added up.*

* *

**9. PASCAL'S TRIANGLE**

** **

* 1*, *6, 15, 20, 15, 6, 1*

* 1*, *7*, *21, 35, 35, 21, 7, 1*

* 1, 8, 28, 56, 70, 56, 28, 8, 1*

* 1, 9, 36, 84, 126, 126, 84, 36, 9, 1*

* *

*10. ***OTHER PATTERNS IN PASCAL'S TRIANGLE**

** **

* Answers will vary*

* *

* *

*Chapter *5, Problem Set B

*1. ***GOLF MATCH**

** **

* Diana will tee off second.*

* *

*2. ***MACARONI AND CHEESE**

** **

* 1/3 of a pound.*

* *

*3. ***COMIC OF THE MONTH**

* $22.42*

* *

* *

*5. ***ROO AND TIGGER**

** **

* Roo by 4 feet.*

* *

*Chapter 6, Problem Set**A*

* *

*1. ***DIMES AND QUARTERS**

** **

* 8 quarters, 13 dimes*

* *

*2. ***MARKDOWN**

** **

* $34.30*

* *

*3. ***TAX**

** **

* $14.49*

* *

* *

*6. ***CHECKING ACCOUNT**

** **

* 39**checks*

* *

* *

*8. ***BASEBALL CARDS**

** **

* 35 cards*

* *

*9. ***STAMPS**

** **

*five 16-cent stamps and seven 7-cent stamps*

* *

*10. ***A BUNCH OF CHANGE**

** **

*14 dimes, 25 nickels, 19 quarters*

* *

*11. ***Special numbers**

** **

* Use guess and check. *

* *

*12. ***After the football game**

** **

* 15 people*

* *

*13. ***TRAVELING TO MOM'S HOUSE**

** **

* 28 miles*

* *

*14. ***RIDING A HORSE**

** **

* 3 miles per hour*

* *

* *

*15. ***Shopping Surprises**

** **

* $3.00 per dozen.*

* *

* *

* *

*Chapter 6, Problem Set B*

*1. ***Football Scores**

* 14 ways (when order is important).*

* *

*2. ***Animals**

* Use guess and check technique. Hint: lots of rabbits.*

* *

*5. ***LARRY LONGWAY AGAIN**

* 3, 3, and 8*

**6. ** **Cakes and Tea**

* 7 people, 2 cakes, 3 (cups of ) tea.*

* *

*Chapter 7, Problem Set**A*

* *

*1. ***COFFEE**

* 6 ounces (Suggested sub-questions:*

*a. How much does 1 lb of coffee cost?*

b. How much does 1oz of coffee cost?

c. How many oz of coffee can $1.11 buy? )

b. How much does 1oz of coffee cost?

c. How many oz of coffee can $1.11 buy? )

*2. ***SHARING EXPENSES**

* Many answers are possible. Each person's share is $8.l6. Leroy needs $5.84; Max needs 84*¢

*; Alex owes $5. 16; Kulwinder owes $1.16; Bobbi owes 36*¢

*.*

(Suggested sub-questions:

(Suggested sub-questions: