Puzzle Design Challenge

Daniel Lee

Mrs. Laing-IED

i

AutobiographyI was born in Raleigh, North Carolina, on January 4, 1997. I lived in Raleigh for three years until I moved to Zebulon, North Carolina, where I currently reside. At an early age, I became interested in things related to space travel from watching Star Wars and other media of the genre. I began school at Heritage Christian Academy and remained there until 4th grade, where I transferred to Wakelon Elementary School. For junior high, I went to Zebulon GT Magnet Middle School, where I became exposed to more clubs that dealt with engineering and additionally became a musician in the band. After middle school, I enrolled in Southeast Raleigh Magnet High School. I enrolled in the Engineering Academy as a junior, and am aspiring to study Aerospace Engineering as my major.

ii

Puzzle Design Challenge Brief

Client Fine Office Furniture, Inc.

Target Consumer Ages: High school aged

Designer Daniel Lee

Problem Statement

A local office furniture manufacturing company throws away tens of thousands of scrap ¾” hardwood cubes that result from its furniture construction processes. The material is expensive, and the scrap represents a sizeable loss of profit.

Design Statement

Fine Office Furniture, Inc. would like to return value to its waste product by using it as the raw material for desktop novelty items that will be sold on the showroom floor. Design, build, test, document, and present a three-dimensional puzzle system that is made from the scrap hardwood cubes. The puzzle system must provide an appropriate degree of challenge to high school students.

Criteria1. The puzzle must be fabricated from 27 – ¾″ hardwood cubes.

2. The puzzle system must contain exactly five puzzle parts.

3. Each individual puzzle part must consist of at least four, but no more than six hardwood cubes that are permanently attached to each other.

4. No two puzzle parts can be the same.

5. The five puzzle parts must assemble to form a 2 ¼″ cube.

6. Some puzzle parts should interlock.

7. The puzzle should require high school students an average of 3 minutes/ 40 seconds to solve.

1

Possible Part CombinationsBrainstormed and sketched on isometric grid paper possible puzzle part cube combinations for the cube using Activity 4.1a Puzzle Cube Combinations.

3 Piece Cube Combinations:

4 Piece Cube Combinations:

5 Piece Cube Combinations:

2

6 Piece Combinations:

Puzzle Cube DesignsTwo different Puzzle Cube designs were created from the possible parts using Activity 4.1b Graphical Modeling. For each design, isometric views of each of the five component parts were neatly sketched and color coded and showed how they fit together in the isometric view of the cube on isometric grid paper. A total of two solutions with ten unique parts were used.

The solution on the left hand side was made to be solved with a low level of difficulty while the right hand side was made to be solved with a high level of difficulty. The

3

solution with the highest level of difficulty was chosen to be built because that’s what our teacher told us to do.

Multi-view SketchesFully dimensioned multi-view sketches of the puzzle parts were made.

Inventor Multi-View SketchesFully dimensioned multi-view sketches of the puzzle parts were made in inventor.

4

5

6

Block Assembly (Inventor)

7

8

9

Block Assembly (Wood Pieces)

10

Solving Time Data and StatisticsTen subjects were tested to determine the amount of time it takes to solve the puzzle. Each subject was given three attempts at solving the puzzle and each subject was timed until all five pieces were placed into the correct position.

First Attempt Data:

Solving Time (Min.)Solving Time (Decimal Min.) Gender Class

4:17 4.283 M Sophmore2:03 2.05 F Junior4:24 4.4 M Freshman2:53 2.883 F Senior3:15 3.25 M Senior4:48 4.8 F Freshman3:09 3.15 M Junior4:53 4.883 F Freshman4:53 4.883 M Sophmore2:06 2.1 F Senior

Mean= 3.6682

11

Median= 3.7665Mode= 4.883Stdv p= 1.062249669stdv s= 1.119709466Range= 2.833

Second Attempt Data:Solving Time (Min.) Soliving Time (Decimal Min.) Gender Class

1:06 1.1 MSophmore

1:12 1.2 F Junior1:52 1.87 M Freshman1:47 1.78 F Senior1:24 1.4 M Senior1:29 1.48 F Freshman1:02 1.03 M Junior1:05 1.08 F Freshman

1:47 1.78 MSophmore

1:11 1.18 F SeniorMean= 1.39

Third Attempt Data:Solving Time (Min.)

Solving Time (Decimal Min.) Gender Class

0:51 0.85 MSophmore

0:26 0.43 F Junior0:50 0.83 M Freshman0:59 0.98 F Senior0:49 0.8167 M Senior0:12 0.2 F Freshman0:16 0.27 M Junior0:45 0.75 F Freshman

0:30 0.5 MSophmore

0:23 0.38 F SeniorMean= 0.60067

1

12

Number of Attempts vs Average Solution Time

1 2 30

0.5

1

1.5

2

2.5

3

3.5

43.6682

1.39

0.60067

Number of Attempts

Aver

age

Solu

tion

Tim

e (D

ecim

al M

in.)

F(x) = -1.5338x + 4.9538 x = number of attempts F(x) = Average Solution Time

The slope is -1.5338 meaning that for every attempt made on the puzzle cube, the solving time will go down by 1.5338 minutes. The y-intercept is 4.9538. However, that really has no correlation with anything because you can’t have a solving time if you’ve never even attempted the puzzle.

Average solving time on the fifth attempt:

F (5) = -1.5338 (5) + 4.9538 = -2.7152

1 2 30

0.5

1

1.5

2

2.5

3

3.5

43.6682

1.39

0.60067

f(x) = − 1.533765 x + 4.95382

Number of Attempts

Aver

age

Solu

tion

Tim

e (D

ecim

al M

in.)

Number of attempts for 23 seconds:

0.23 = -1.5338x + 4.9538

X = 3.0

13

Test Result SummaryThe average solution time on a first attempt appeared to be 3 minutes and 40

seconds. One male and one female were chosen from each class level to obtain data variety. On a first attempt juniors appeared to do the best in terms of class level, and females did better than males. The data for the second showed that juniors still did fairly well compared to others. However, the results were mixed for the rest of the classes. Being male or female didn’t prove to factor in this attempt. The data for the third attempt showed that juniors still most likely had the best solution times when grouped together. Just like with attempt #2, the other class levels yielded mixed results compared to their other attempts. A majority of the males had low times when looked at as a group; however, the females didn’t have much better times. Ultimately, juniors had the fastest solving times.

Based on the test results, the puzzle meets the criteria from the design brief. It proved to be a challenge for high school students of all ages to put together. It also met all the specifications for its assembly design.

Possible ImprovementsThis cube definitely could have been made more difficult. I wasn’t sure how hard

to make it at first because I didn’t know how what was hard to others. However, now that I have a standard to work with, I realize the puzzle cube could have been made harder in the sense that I could have used more complicated puzzle parts.

Conclusion Questions1. Why is it important to model an idea before making a final prototype?

It’s important to model and idea because you need the exact measurements beforehand to make an accurate working model like a prototype.

2. Which assembly constraint(s) did you use to constrain the parts of the puzzle to the assembly such that it did not move? Describe each of the constraint types used and explain the degrees of freedom that are removed when each is applied between two parts. You may wish to create a sketch to help explain your description.

I didn’t use any constraints to put my model together. I used the joint command to manually fit the corners with each other so that they stuck together. However, you can use the mate and flush commands to constrain the assembly to movements in certain planes. For example I could use the flush command to constrain a face of the pink part to the blue part. This would cause the pink part’s face to always be pointed in the direction of the blue part. This also causes two degrees of freedom to be removed

14

3. Based on your experiences during the completion of the Puzzle Design Challenge, what is meant when someone says, “I used a design process to solve the problem at hand”? Explain your answer using the work that you completed for this project.

When someone says “I used a design process to solve the problem at hand”, they mean the used a process of six steps: identifying the problem, generating concepts, developing solutions, constructing and testing a prototype, evaluating the solution, and finally presenting the solution. I also used this process to develop a solution to the puzzle cube. I identified the problem by studying the constraints of the design brief and looking at other examples of the design challenge. Concepts were generated with activity 4.1a when all the possible puzzle cube parts I could think of were being created. Solutions were developed in 4.1b when I created two possible puzzle cube combinations. Using ¾” wood blocks, I constructed a prototype of the block and tested it with 10 people. After evaluating it with solution times and debating the overall look of the cube, I am now presenting it in this design portfolio.

4. How does the gender of the puzzle solver affect solution time? Be specific and provide evidence to support your answer.

Based on the test results, females seemed to be more adept at figuring out the puzzle on a first attempt, but not by a very big margin.

5. How does the age of the puzzle solver affect solution time?

a. Make a specific statement related to the rate of increase or decrease of solution time with respect to age. Provide evidence that supports your statement.

The solution time of an individual decreases by 42 seconds for every increase in age.

b. Write an equation using function notation that represents puzzle solution time in terms of age. Be sure to define your variables and identify units.

F(x) = -0.702x + 14.887 x = age F(x) = solution time

c. Predict the solution time on the first attempt of a child who is 3 years of age. Show your work.

F (3) = -0.702(3) + 14.887 = -2.106 + 14.887 = 12.781 minutes

d. Predict the solution time on the first attempt of a person who is 95 years of age. Show your work.

F (95) = -0.702(95) + 14.887 = -66.69 + 14.887 = -51.803 minutes

e. Do these predictions make sense? Why or why not?

These predictions don’t make sense. A really smart 3 year old might be able to solve the puzzle with some luck in 12 minutes. However, it’s not possible to

15

have negative minutes because time doesn’t work like that. A 95 year old would never be able to get that solution time.

f. What is a realistic domain for the function?

The realistic domain of the function should be 13<x<19. This is the case because this equation was made from the data of high school students. Therefore, the realistic domain would be the ages for high school students only.