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Practice GuideVersion 1.0 - Covers challenges 1 to 30

Let’s practice!Welcome to the Turing Tumble Practice Guide! This is a free companion to TuringTumble. This version of the guide covers the first 30 challenges in the book. If it’suseful, we’ll do the same for the rest of the challenges.The purposes of this guide are:1. To cement important concepts. Practice challenges give another opportunity toapply what you learned.2. To offer hints when you’re stuck. Solve a practice challenge or read theexplanation of the solution. This guide lowers the learning curve.3. To learn how puzzle solutions work. Each solution has an explanation thatdescribes how it works.4. To offer the puzzles in an easily printable black and white format. Make asmany copies as you like.What is the best way to use this practice guide?The practice guide is meant to be used alongside the Turing Tumble puzzle book,but it’s not meant to replace it. Unlike the Turing Tumble puzzle book, it doesn’tcontain instructions for how to assemble the computer, how to play, how the partswork, and other bits of useful information.Is this guide useful to you?Please tell us what you think! We’re always looking for ways to make TuringTumble better. Just send us an email at [email protected] you find an error?Please send a quick email to [email protected] and we’ll fix it right away. Wedon’t like bugs.

ContentsChallenge 1.1Practice Puzzle A for Challenge 2.3Challenge 2.5Practice Puzzle A for Challenge 3.7Challenge 3.9Practice Puzzle A for Challenge 4. 11Practice Puzzle B for Challenge 4. 13Challenge 4. 15Practice Puzzle A for Challenge 5. 17Challenge 5.19Practice Puzzle A for Challenge 6. 21Challenge 6. 23Practice Puzzle A for Challenge 7. 25Challenge 7. 27Practice Puzzle A for Challenge 8.29Challenge 8. 31Practice Puzzle for Challenge 9. 33Challenge 9. 35Challenge 10. 37Practice Puzzle A for Challenge 11.39Challenge 11.41Challenge 12.43Challenge 13.45Challenge 14. 47Practice Puzzle A for Challenge 15.49Practice Puzzle B for Challenge 15. 51Challenge 15. 53Practice Puzzle A for Challenge 16.55Practice Puzzle B for Challenge 16. 57Practice Puzzle C for Challenge 16.59Challenge 16.61Practice Puzzle A for Challenge 17.63

Practice Puzzle B for Challenge 17.65Challenge 17. 67Practice Puzzle A for Challenge 18.69Challenge 18. 71Challenge 19. 73Challenge 20. 75Practice Puzzle A for Challenge 21. 77Challenge 21. 79Practice Puzzle A for Challenge 22.81Challenge 22.83Practice Puzzle A for Challenge 23.85Practice Puzzle B for Challenge 23.87Practice Puzzle C for Challenge 23. 89Challenge 23.91Challenge 24.93Challenge 25.95Challenge 26. 97Practice Puzzle A for Challenge 27.99Practice Puzzle B for Challenge 27. 101Challenge 27. 103Practice Puzzle A for Challenge 28. 105Challenge 28. 107Challenge 29.109Bonus Puzzle A for Challenge 29. 111Challenge 30. 113

Turing Tumble Practice Guide 1.0Challenge 1: GravityObjective: Make all of the blue balls (and only the blue balls) reachthe end.Required output:Starting setupx8Available partsx8x4PRESSTOSTART1

Turing Tumble Practice Guide 1.0Challenge 1 SolutionExplanation: The four ramps complete the path from the top of theboard to the bottom of the board.Remember that it’s against the rules to allow balls to fall freely forany distance! When a ball rolls off a part, it must immediately land onthe next part.x8PRESSTOSTART2x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 2Objective: Make all of the blue balls (and only the blue balls) reachthe end.Required output:Starting setupx8Available partsx8x3PRESSTOSTART3

Turing Tumble Practice Guide 1.0Practice Challenge 2-A SolutionExplanation: The ramps ﬁll the gaps in the path from the top of theboard to the bottom of the board.x8PRESSTOSTART4x8

Turing Tumble Practice Guide 1.0Challenge 2: Re-entryObjective: Make all of the blue balls (and only the blue balls) reachthe end.Required output:Starting setupx8Available partsx8x5PRESSTOSTART5

Turing Tumble Practice Guide 1.0Challenge 2 SolutionExplanation: The starting setup leads the balls over onto the rightside. That’s a problem! If the balls hit the right lever, they’d releasered balls, but you’re only supposed to let the blue balls get to thebottom.To solve this puzzle, you have to use the 5 ramps to lead balls backover to the left lever.x8PRESSTOSTART6x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 3Objective: Start the machine by releasing the blue ball. The blue ballshould then release the red ball.Required output:Starting setupx1Available partsx1x8PRESSTOSTART7

Turing Tumble Practice Guide 1.0Practice Challenge 3-A SolutionExplanation: The 8 ramps make a path down to the right lever. Whenthe blue ball is released, it lands on the right lever, releasing the redball.x1PRESSTOSTART8x1

Turing Tumble Practice Guide 1.0Challenge 3: IgnitionObjective: Release one blue ball and then all of the red balls.Required output:Starting setupx8Available partsx8x6PRESSTOSTART9

Turing Tumble Practice Guide 1.0Challenge 3 SolutionExplanation: Like the last puzzle, the ramps bring the paths of thered and blue balls into one path that leads to the right lever. After theﬁrst blue ball, all the rest are red.x8PRESSTOSTART10x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 4Objective: Release one blue ball and then all of the red balls.Required output:Starting setupx8Available partsx8x6PRESSTOSTART11

Turing Tumble Practice Guide 1.0Practice Challenge 4-A SolutionExplanation: The paths of the blue and red balls come together nearthe bottom of the board and then lead to the red side. Since all pathslead to the red side, only red balls are released after the ﬁrst blueball.x8PRESSTOSTART12x8

Turing Tumble Practice Guide 1.0Practice Puzzle B for Challenge 4Objective: Release one red ball and then all of the blue balls.Required output:Starting setupx8Available partsx8x6PRESSTOSTART13

Turing Tumble Practice Guide 1.0Practice Challenge 4-B SolutionExplanation: This is just like challenge 3, but everything is reversed!Notice that the “Presser” is on the right side, not the left, so you startthe machine by pressing down the right lever. That makes the ﬁrstball red.x8x8PRESSTOSTART14

Turing Tumble Practice Guide 1.0Challenge 4: FusionObjective: Release one red ball and then all of the blue balls.Required output:Starting setupx8Available partsx8x 13PRESSTOSTART15

Turing Tumble Practice Guide 1.0Challenge 4 SolutionExplanation: The paths need to come together, but they start farapart! Use the ramps to bring the paths together and lead all of theballs to the left side.x8x8PRESSTOSTART16

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 5Objective: Make the pattern blue, red, blue, red, blue, red.Required output:Starting setupx8Available partsx8x1PRESSTOSTART17

Turing Tumble Practice Guide 1.0Practice Challenge 5-A SolutionExplanation: To get the alternating pattern, blue balls have to get tothe right side to release red balls, and red balls have to get to the leftside to release blue balls. The paths have to cross over each other!Where they cross, use the crossover part.x8PRESSTOSTART18x8

Turing Tumble Practice Guide 1.0Challenge 5: EntropyObjective: Make the pattern blue, red, blue, red, blue, red.Required output:Starting setupx8Available partsx8x9PRESSTOSTART19

Turing Tumble Practice Guide 1.0Challenge 5 SolutionExplanation: This time, you have to create your own path for the redballs to get over to the left lever! You must use the crossover whereyour path crosses the path of the blue balls.x8PRESSTOSTART20x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 6Objective: Make the pattern blue, red, blue, red, blue, red.Required output:Starting setupx8Available partsx8x3PRESSTOSTART21

Turing Tumble Practice Guide 1.0Practice Challenge 6-A SolutionExplanation: In this puzzle, the red and blue paths cross each otherthree times! At each point where they cross, you must place a crossover.x8PRESSTOSTART22x8

Turing Tumble Practice Guide 1.0Challenge 6: Total Internal ReﬂectionObjective: Make the pattern blue, red, blue, red, blue, red.Required output:Starting setupx8Available partsx8x2x5PRESSTOSTART23

Turing Tumble Practice Guide 1.0Challenge 6 SolutionExplanation: The paths for the red and blue balls cross over eachother ﬁve times. Crossovers must be placed at each point where theycross.In the last two puzzles, the paths crossed each other one and threetimes. One, three, and ﬁve are all odd numbers. What would happenif the paths crossed over each other an even number of times?x8PRESSTOSTART24x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 7Objective: Create a path for the blue balls to reach the output withonly 6 ramps.Required output:Starting setupx8Available partsx8x6PRESSTOSTART25

Turing Tumble Practice Guide 1.0Practice Challenge 7-A SolutionExplanation: At the top, you’ve got to decide, “Do I go to the left or tothe right?” The right is the better path because you can use twocrossovers instead of just one.x8PRESSTOSTART26x8

Turing Tumble Practice Guide 1.0Challenge 7: Path of Least ResistanceObjective: Create a path for the blue balls to reach the output withonly 6 ramps.Required output:Starting setupx8Available partsx8x6PRESSTOSTART27

Turing Tumble Practice Guide 1.0Challenge 7 SolutionExplanation: This one is a little tricker than the last challenge. At thetop, you must make a choice on whether to go to the left or to theright. You must go to the left this time.x8PRESSTOSTART28x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 8Objective: Make all of the blue balls (and only the blue balls) reachthe end.Required output:Starting setupx8Available partsx8x2PRESSTOSTART29

Turing Tumble Practice Guide 1.0Practice Challenge 8-A SolutionExplanation: The bit sends the blue balls in alternating directions.First right, then left, then right, and so on. You must add ramps oneither side of the bit to get the balls to a path that leads to thebottom.x8PRESSTOSTART30x8

Turing Tumble Practice Guide 1.0Challenge 8: DepolarizationObjective: Make the pattern blue, red, blue, red, blue, red.Required output:Starting setupx8Available partsx8x 14PRESSTOSTART31

Turing Tumble Practice Guide 1.0Challenge 8 SolutionExplanation: A bit is used to alternate the color of the balls released.x8PRESSTOSTART32x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 9Objective: Make the pattern blue, blue, red, blue, blue, red.Required output:Starting setupx 10Available partsx 10x 13PRESSTOSTART33

Turing Tumble Practice Guide 1.0Practice Challenge 9-A SolutionExplanation: The bit only lets every other blue ball reach the rightlever, but every red ball ends at the left lever.x 10PRESSTOSTART34x 10

Turing Tumble Practice Guide 1.0Challenge 9: DimersObjective: Make the pattern blue, blue, red, blue, blue, red.Required output:Starting setupx 10Available partsx 10x 18PRESSTOSTART35

Turing Tumble Practice Guide 1.0Challenge 9 SolutionExplanation: Just like the last puzzle, the bit makes every other blueball release a red ball, but every red ball releases a blue ball.Do you see how the bit splits the path of the blue balls to go in twodirections? This is very important in the coming puzzles!x 10PRESSTOSTART36x 10

Turing Tumble Practice Guide 1.0Challenge 10: Double BondObjective: Make the pattern blue, blue, red, red, blue, blue, red, red Required output:Starting setupx8Available partsx8x 22PRESSTOSTART37

Turing Tumble Practice Guide 1.0Challenge 10 SolutionExplanation: This time, there are bits in the path of both the red andblue balls. The bits cause only every other ball to cross to the otherside of the board.x8PRESSTOSTART38x8

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 11Objective: Flip bits A and B to the right.Starting setupAvailable partsx0x2Ax 15BPRESSTOSTART39

Turing Tumble Practice Guide 1.0Practice Challenge 11-A SolutionExplanation: The top bit is used to distribute the blue balls betweentwo paths - one leads to the left bit and the other leads to the rightbit.x0x2APRESSTOSTART40B

Turing Tumble Practice Guide 1.0Challenge 11: SelectivityObjective: Flip bits 2 and 5 to the right.Starting setupAvailable partsx0x21234x 155PRESSTOSTART41

Turing Tumble Practice Guide 1.0Challenge 11 SolutionExplanation: The top bit splits the path of the blue balls. One pathleads to bit 2 and the other path leads to bit 5.x0x21PRESSTOSTART422345

Turing Tumble Practice Guide 1.0Challenge 12: Duality - Part 1Objective: Intercept a blue ball.Starting setupx8Available partsx8x3PRESSTOSTART43

Turing Tumble Practice Guide 1.0Challenge 12 SolutionExplanation: The ramps must be used to complete the path of asingle ball to the interceptor.x8PRESSTOSTART44x8

Turing Tumble Practice Guide 1.0Challenge 13: Duality - Part 2Objective: Intercept a red ball.Starting setupx8Available partsx8x 12PRESSTOSTART45

Turing Tumble Practice Guide 1.0Challenge 13 SolutionExplanation: Even though you start by releasing a blue ball, you’vegot to get a red ball in the interceptor. How do you do that?Here’s how: Lead the ﬁrst blue ball to the right lever, releasing a redball. Then lead the red ball to the interceptor with ramps.x8PRESSTOSTART46x8

Turing Tumble Practice Guide 1.0Challenge 14: Duality - Part 3Objective: If the machine starts with bit A pointing to the left, intercept a blue ball. Otherwise, intercept a red ball.Examples:IfAthenIfAthenStarting setupAvailable partsx8x8x 20APRESSTOSTART47

Turing Tumble Practice Guide 1.0Challenge 14 SolutionExplanation: Let’s think about each of the two starting conditionsseparately.A starts left:Like puzzle 12, theﬁrst blue ball simplyfalls into theinterceptor.A starts right:Like puzzle 13, theﬁrst blue ball fallsonto the lever on theright side of theboard, releasing ared ball that lands inthe interceptor.Ax8x8APRESSTOSTART48A

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 15Objective: Let only one blue ball reach the end. Intercept the 2nd ball.Required output:Starting setupx8Available partsx8x 12x1PRESSTOSTART49

Turing Tumble Practice Guide 1.0Practice Challenge 15-A SolutionExplanation: Use the bit to make the ﬁrst ball take a path that leadsto the bottom and the second ball take a path to the interceptor.x8PRESSTOSTART50x8

Turing Tumble Practice Guide 1.0Practice Puzzle B for Challenge 15Objective: If bit A starts to the left, intercept a red ball. If bit A startsto the right, intercept a blue ball.Examples:IfAthenIfAthenStarting setupAvailable partsx8x8x 11APRESSTOSTART51

Turing Tumble Practice Guide 1.0Practice Challenge 15-B SolutionExplanation: This one is tricky! Bit A is all the way at the bottom ofthe board. How can you set the color of the ball that goes in aninterceptor based on a bit that is below the interceptor?You need to send information up the board! There are two ways to dothat. The ﬁrst way (the way we do it here) is to use the right and leftlevers. The color of the second ball released from the top will tell youthe direction the bit at the bottom was pointing.The second way to send information up the board is with gears andgear bits. We’ll get to that later. :)x8x8APRESSTOSTART52

Turing Tumble Practice Guide 1.0Challenge 15: InversionObjective: If bit A starts to the left, intercept a blue ball. If bit A startsto the right, intercept a red ball.Examples: A AStarting setupAvailable partsx8x8x 11x2APRESSTOSTART53

Turing Tumble Practice Guide 1.0Challenge 15 SolutionExplanation: Like the previous puzzle, the bit at the bottom of theboard decides the color of the ball that must go in the interceptor. Butfor this puzzle, the colors are reversed! Here we do that with acarefully placed crossover.x8x8APRESSTOSTART54

Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 16Objective: Catch the 1st blue ball in the interceptor.Starting setupx8Available partsx8x1PRESSTOSTART55

Turing Tumble Practice Guide 1.0Practice Challenge 16-A SolutionExplanation: Since both bits start pointed to the right, you only needto add a single ramp to ﬁnish the path to the interceptor.x8PRESSTOSTART56x8

Turing Tumble Practice Guide 1.0Practice Puzzle B for Challenge 16Objective: Let only 1 blue ball reach the bottom and catch the 2nd ballin the interceptor.Required output:Starting setupx8Available partsx8x3PRESSTOSTART57

Turing Tumble Practice Guide 1.0Practice Challenge 16-B SolutionExplanation: The top bit sends the ﬁrst ball to the right, which leadsto the left lever. Then, when the second ball is released, both bitspoint right, just like in the previous challenge. The second ball travelsto the interceptor.x8PRESSTOSTART58x8

Practice Puzzle C for Challenge 16Turing Tumble Practice Guide 1.0Practice Puzzle C for Challenge 16Objective: Let only 2 blue balls reach the bottom and catch the 3rdball in the interceptor.Required output:Starting setupx8Available partsx8x3x1PRESSTOSTART59

Turing Tumble Practice Guide 1.0Practice Challenge 16-C SolutionExplanation: Think about the direction the bits are pointing wheneach ball is released:1st ball2nd ball3rd ballNotice that the top bit ﬂips with every ball, but the bottom bit onlyﬂips when the top bit points left.x8PRESSTOSTART60x8

Challenge 16Turing Tumble Practice Guide 1.0Challenge 16: TerminationObjective: Let only 3 blue balls reach the bottom and catch the 4thball in the interceptor.Required output:Starting setupx8Available partsx8x 10PRESSTOSTART61

Turing Tumble Practice Guide 1.0Challenge 16 SolutionExplanation: Like the previous puzzle, think about the direction thebits point when each ball is released:1st ball2nd ball3rd ball4th ballThe way these bits count out balls is important! You’ll use it manytimes in the coming puzzles.x8PRESSTOSTART62x8

Practice Puzzle A for Challenge 17Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 17Objective: Let only 3 red balls reach the bottom and catch the 4thball in the interceptor.Required output:Starting setupx8Available partsx8x 10PRESSTOSTART63

Turing Tumble Practice Guide 1.0Practice Challenge 17-A SolutionExplanation: This puzzle demonstrates how you can ﬂip the solutionto the previous puzzle around and get the same thing.x8x8PRESSTOSTART64

Practice Puzzle B for Challenge 17Turing Tumble Practice Guide 1.0Practice Puzzle B for Challenge 17Objective: Make the pattern blue, red, red, red.Required output:Starting setupx8Available partsx8x 16PRESSTOSTART65

Turing Tumble Practice Guide 1.0Practice Challenge 17-B SolutionExplanation: Here you can kick off the computer by releasing a blueball that travels to the right lever and releases a red ball. The red ballstarts the two bit counter (just like the previous puzzle) that stopsafter 4 red balls are released.x8PRESSTOSTART66x8

Challenge 17Turing Tumble Practice Guide 1.0Challenge 17: Fixed RatioObjective: Make the pattern blue, blue, blue, red, red, red.Required output:Starting setupx8Available partsx8xPRESSTOSTART67

Turing Tumble Practice Guide 1.0Challenge 17 SolutionExplanation: Now we have two 2-bit counters - one on the left andone on the right. Notice the starting positions of the bits! To get threeblues and three reds in the output, we have to count out 3 blue balls,and 4 red balls (the 4th ball goes into the interceptor!).x8PRESSTOSTART68x8

Practice Puzzle A for Challenge 18Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 18Objective: If both bits start pointed to the right, put a ball in interceptor T. Otherwise put a ball in interceptor F.Examples:A AFTBORABORBA TBStarting setupAvailable partsx8x8Fx3TFPRESSTOSTART69

Turing Tumble Practice Guide 1.0Practice Challenge 18-A SolutionExplanation: When both bits point right, it’s a straight shot tointerceptor T. Your job is to add ramps to get the ball to interceptor Fwhen either one of the bits start pointed left.x8x8TFPRESSTOSTART70

Challenge 18Turing Tumble Practice Guide 1.0Challenge 18: EntanglementObjective: If the top bit AND the bottom bit start pointed to the right,put a ball in interceptor T. Otherwise put a ball in interceptor F.Examples:A ATFBORABORBA TBStarting setupAvailable partsx8x8TFx7FPRESSTOSTART71

Turing Tumble Practice Guide 1.0Challenge 18 SolutionExplanation: This puzzle is the same as the last puzzle, except thatthe path the ball must take in each case is a little different.x8PRESSTOSTART72x8

Challenge 19Turing Tumble Practice Guide 1.0Challenge 19: EntanglementObjective: If the top bit AND the bottom bit start pointed to the right,intercept a blue ball. Otherwise, intercept a red ball.Examples:AB AA BB ABStarting setupx8 Available partsx8xx2PRESSTOSTART73

Turing Tumble Practice Guide 1.0Challenge 19 SolutionExplanation: This time there is only one interceptor. Instead of sending the ball to interceptor F if the bits aren’t both pointed right, youmust direct the ball to the right lever. Then direct the red ball that’sreleased to the interceptor.x8PRESSTOSTART74x8

Challenge 20Turing Tumble Practice Guide 1.0Challenge 20: SymbiosisObjective: If the top bit OR the bottom bit start pointed to the right,intercept a blue ball. Otherwise, intercept a red ball.Examples:AB AA BB ABStarting setupx8 Available partsx8xx2PRESSTOSTART75

Turing Tumble Practice Guide 1.0Challenge 20 SolutionExplanation: It’s easiest to consider the ﬁrst condition - when bothbits are pointed left. Make that path go directly to the red lever andmake a path for the red ball to go directly to the interceptor. Thenmake every other possible path for that ﬁrst blue ball lead to theinterceptor.x8PRESSTOSTART76x8

Practice Puzzle A for Challenge 21Turing Tumble Practice Guide 1.0Practice Puzzle A for Challenge 21Objective: Each register below shows a number. Can you ﬁgure outwhat number is shown by each one?Examples:121 0241 14A1 241 24A5A12 4AA111222 444888A 4A A2A77

Turing Tumble Practice Guide 1.0Practice Challenge 21-A SolutionExplanation: Remember - to ﬁgure out the number shown, simplyadd the number next to each bit that is pointed right.A. How many numbers can be represented by a 3-bit register?B. How many numbers can be represented by a 4-bit register?C. What is the smallest number that can be represented on a 4-bitregister?D. What is the largest number that can be represented on a 4-bitregister?A. 8 B. 16 C. 0 D. 15121 2246211222 12444888A7 15A19 4A 78 4AA1A

Challenge 21Turing Tumble Practice Guide 1.0Challenge 21: Quantum NumberObjective: Use register A to count the number of blue balls. (Use 15 orless balls.)Examples:x5 A 5x 14 A 14x7 A 7x 11A 11 Starting setupAvailable partsx0x*x51248APRESSTOSTART79

Turing Tumble Practice Guide 1.0Challenge 21 SolutionExplanation: This seems a lot more complicated than it really is!The top bit ﬂips with every ball.The

The practice guide is meant to be used alongside the Turing Tumble puzzle book, but it’s not meant to replace it. Unlike the Turing Tumble puzzle book, it doesn’t contain instructions for how to assemble the computer, how to play, how the parts work, and other bits of useful information.