EducatorGuide.md

Turing Tumble Educator Guide

Solutions to all Turing Tumble puzzles in the Educator Guide (see the notation used in the solutions).

• Challenge #1: Gravity
• Challenge #2: Re-entry
• Challenge #3: Ignition
• Challenge #4: Fusion
• Challenge #5: Entropy
• Challenge #6: Total Internal Reflection
• Challenge #7: Path of Least Resistance
• Challenge #8: Depolarization
• Challenge #9: Dimers
• Challenge #10: Double Bond
• Challenge #11: Selectivity
• Challenge #12: Duality - Part 1
• Challenge #13: Duality - Part 2
• Challenge #14: Duality - Part 3
• Challenge #15: Inversion
• Challenge #16: Termination
• Challenge #17: Fixed Ratio
• Challenge #18: Entanglement
• Challenge #19: Entanglement
• Challenge #20: Symbiosis
• Challenge #21: Quantum Number
• Challenge #22: Depletion
• Challenge #23: Tetrad
• Challenge #24: Ennead
• Challenge #25: Regular Expression
• Challenge #26: Nucleus
• Challenge #27: Reflection
• Challenge #28: Latch
• Challenge #29: One-Shot Switch
• Challenge #30: Overflow

Challenge #1: Gravity

Objective

Make all of the blue balls (and only the blue balls) reach the end.

Setup

balls:8B-8R; start:B; trace:8B

Solution

 ___o    ___
|  .\. .-.  |
| .-./.-.-. |
|.-.\.-.-.-.|
|-.-./.-.-.-|
|.-.\.-.-.-.|
|-.-./.-.-.-|
|.-.\.-.-.-.|
|-.-./.-.-.-|
|.-.\.-.-.-.|
|-.-./.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #2: Re-entry

Objective

Make all of the blue balls (and only the blue balls) reach the end.

Setup

balls:8B-8R; start:B; trace:8B

Solution

 ___o    ___
|  .\. .-.  |
| .-.\.-.-. |
|.-.-.\.-.-.|
|-.-.-.\.-.-|
|.-.-.-.\.-.|
|-.-.-.-.\.-|
|.-.-.-.-./.|
|-.-.-.-./.-|
|.-.-.-./.-.|
|-.-.-./.-.-|
|     /     |
|____% %____|

Diagram

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Challenge #3: Ignition

Objective

Release one blue ball and then all of the red balls.

Setup

balls:8B-8R; start:B; trace:8RB

Solution

 ___o    ___
|  .\. ./.  |
| .-.\./.-. |
|.-.-.\.-.-.|
|-.-.-.\.-.-|
|.-.-.-.\.-.|
|-.-.-.-.\.-|
|.-.-.-.-./.|
|-.-.-.-.\.-|
|.-.-.-.-./.|
|-.-.-.-.\.-|
|     -     |
|____% %____|

Diagram

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Challenge #4: Fusion

Objective

Release one red ball and then all of the blue balls.

Setup

balls:8B-8R; start:R; trace:8BR

Solution

 ___    o___
|  ./. .\.  |
| ./.-.-.\. |
|./.-.-.-.\.|
|\.-.-.-.-./|
|.\.-.-.-./.|
|-.\.-.-./.-|
|.-.\.-./.-.|
|-.-.\./.-.-|
|.-.-./.-.-.|
|-.-./.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #5: Entropy

Objective

Make the pattern blue, red, blue, red, blue, red…

Setup

balls:8B-8R; start:B; trace:8(RB)

Solution

 ___o    ___
|  .\. ./.  |
| .-.\./.-. |
|.-.-.X.-.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #6: Total Internal Reflection

Objective

Make the pattern blue, red, blue, red, blue, red…

Setup

balls:8B-8R; start:B; trace:8(RB)

Solution

 ___o    ___
|  .\. ./.  |
| .-.\./.-. |
|.-.-.X.-.-.|
|-.-.\./.-.-|
|.-.-.X.-.-.|
|-.-.\./.-.-|
|.-.-.X.-.-.|
|-.-.\./.-.-|
|.-.-.X.-.-.|
|-.-.\./.-.-|
|     X     |
|____% %____|

Diagram

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Challenge #7: Path of Least Resistance

Objective

Create a path for the blue balls to reach the output with only 6 ramps.

Setup

balls:8B-8R; start:B; trace:8B

Solution

 ___o    ___
|  .\. .-.  |
| .-./.-.-. |
|.-.X.X.-.-.|
|-./.-.-.-.-|
|.X.-.-.-.-.|
|\.-.X.-.-.-|
|.\.-.-.-.-.|
|-.X.-.-.-.-|
|.-.X.-.-.-.|
|-.-./.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #8: Depolarization

Objective

Make the pattern blue, red, blue, red, blue, red…

Setup

balls:8B-8R; start:B; trace:8(RB)

Solution

 ___o    ___
|  .\. ./.  |
| .-.\./.-. |
|.-.-.<.-.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #9: Dimers

Objective

Make the pattern blue, blue, red, blue, blue, red…

Setup

balls:10B-10R; start:B; trace:5(RBB)

Solution

 ___o    ___
|  .>. ./.  |
| .\.\./.-. |
|.-.\.X.-.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #10: Double Bond

Objective

Make the pattern blue, blue, red, red, blue, blue, red, red…

Setup

balls:8B-8R; start:B; trace:4(RRBB)

Solution

 ___o    ___
|  .>. .<.  |
| .\.\././. |
|.-.\.X./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #11: Selectivity

Objective

Flip bits 2 and 5 to the right.

Setup

balls:2B-0R; start:B; trace:BB

Solution

 ___o    ___
|  .\. .-.  |
| .-.\.-.-. |
|.-.-.>.-.-.|
|-.-./.\.-.-|
|.-./.-.\.-.|
|-.\.-.-.\.-|
|.<.<.<.<.<.|
|-.-./.-.-./|
|.-./.-.-./.|
|-./.-.-./.-|
|     -     |
|____% %____|

Diagram

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Challenge #12: Duality - Part 1

Objective

Intercept a blue ball.

Setup

balls:8B-8R; start:B; trace:b

Solution

 ___o    ___
|  .\. .-.  |
| .-.\.-.-. |
|.-.-.<.-.-.|
|-.-.-.\.-.-|
|.-.-.-.\.-.|
|-.-.-.-./.-|
|.-.-.-./.-.|
|-.-.-./.-.-|
|.-.-.U.-.-.|
|-.-.-.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #13: Duality - Part 2

Objective

Intercept a red ball.

Setup

balls:8B-8R; start:B; trace:rB

Solution

 ___o    ___
|  .\. .\.  |
| .-.\.-./. |
|.-.-.>./.-.|
|-.-./.\.-.-|
|.-./.-.\.-.|
|-./.-.-./.-|
|.\.-.-./.-.|
|-.\.-./.-.-|
|.-.\.U.-.-.|
|-.-.\.-.-.-|
|     \     |
|____% %____|

Diagram

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Challenge #14: Duality - Part 3

Objective

If the machine starts with bit A pointing to the left, intercept a blue ball. Otherwise, intercept a red ball.

Setup

balls:8B-8R; start:B; trace:b|rB

Solution

 ___o    ___
|  .\. .\.  |
| .-.\.-./. |
|.-.-.^./.-.| A
|-.-./.\.-.-|
|.-./.-.\.-.|
|-./.-.-./.-|
|.\.-.-./.-.|
|-.\.-./.-.-|
|.-.\.U.-.-.|
|-.-.\.-.-.-|
|     \     |
|____% %____|

Diagram

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Challenge #15: Inversion

Objective

If bit A starts to the left, intercept a blue ball. If bit A starts to the right, intercept a red ball.

Setup

balls:8B-8R; start:B; trace:bB|rB

Solution

 ___o    ___
|  .>. ./.  |
| .\.\./.-. |
|.-./.U.-.-.|
|-.\.-.-.-.-|
|.-./.-.-.-.|
|-.\.-.-.-.-|
|.-.\.-.-.-.|
|-.-.\.-.-.-|
|.-.-.^.-.-.| A
|-.-.\./.-.-|
|     X     |
|____% %____|

Diagram

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Challenge #16: Termination

Objective

Let only 3 blue balls reach the bottom and catch the 4th ball in the interceptor.

Setup

balls:8B-8R; start:B; trace:bBBB

Solution

 ___o    ___
|  .<. .-.  |
| .\.\.-.-. |
|.-.<./.-.-.|
|-.U.\.-.-.-|
|.-.-./.-.-.|
|-.-.\.-.-.-|
|.-.-./.-.-.|
|-.-.\.-.-.-|
|.-.-./.-.-.|
|-.-./.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #17: Fixed Ratio

Objective

Make the pattern blue, blue, blue, red, red, red.

Setup

balls:8B-8R; start:B; trace:r3R3B

Solution

 ___o    ___
|  .<. .<.  |
| ././.\.\. |
|.\.>.-.<./.|
|-./.\.U.\.-|
|.\.-.\.-./.|
|-./.-.\.\.-|
|.\.-.-.\./.|
|-./.-.-.\.-|
|.\.-.-.-./.|
|-./.-.-.\.-|
|     -     |
|____% %____|

Diagram

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Challenge #18: Entanglement

Objective

If the top bit AND the bottom bit start pointed to the right, put a ball in interceptor left. Otherwise put a ball in interceptor right.

Setup

balls:8B-8R; start:B; trace:b

Solution

 ___o    ___
|  .\. .-.  |
| .-.\.-.-. |
|.-.-.^.-.-.|
|-.-.\.\.-.-|
|.-.-.^./.-.|
|-.-./.\.-.-|
|.-.U.-.U.-.|
|-.-.-.-.-.-|
|.-.-.-.-.-.|
|-.-.-.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #19: Entanglement

Objective

If the top bit AND the bottom bit start pointed to the right, intercept a blue ball. Otherwise, intercept a red ball.

Setup 1

balls:8B-8R; start:B; trace:b|rB

Solution 1

 ___o    ___             ___o    ___
|  .\. .\.  |           |  .\. ./.  |
| .-.\.-.\. |           | .-.\.\.-. |
|.-.-.^.-.\.|           |.-.-.^.\.-.|
|-.-.\.\.-./|           |-.-.\.\./.-|
|.-.-.^./.\.|           |.-.-.^.X.-.|
|-.-./.\.-./|           |-.-.\.X./.-|
|.-./.-.\./.|           |.-.-./.\.-.|
|-./.-.-.X.-|           |-.-.\.-./.-|
|.-.\.-./.\.|           |.-.-./.\.-.|
|-.-.\./.-./|           |-.-.\.-./.-|
|     U     |           |     U     |
|____% %____|           |____% %____|

Diagram 1

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Setup 2

balls:8B-8R; start:B; trace:b|rB|rRB|rRRB

Solution 2

 ___o    ___
|  .\. ./.  |
| .-.\./.-. |
|.-.-.^.-.-.|
|-.-.\.\.-.-|
|.-.-.^./.-.|
|-.-.\./.-.-|
|.-.-.X.-.-.|
|-.-.\./.-.-|
|.-.-.X.-.-.|
|-.-.\.\.-.-|
|     U     |
|____% %____|

Diagram 2

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Challenge #20: Symbiosis

Objective

If the top bit OR the bottom bit start pointed to the right, intercept a blue ball. Otherwise, intercept a red ball.

Setup 1

balls:8B-8R; start:B; trace:b|rB

Solution 1

 ___o    ___
|  .\. .\.  |
| .-.\.-.\. |
|.-.-.^.-.\.|
|-.-././.-./|
|.-.\.^.-.\.|
|-.-./.\.-./|
|.-.\.-.\./.|
|-.-./.-.X.-|
|.-.\.-./.\.|
|-.-.\./.-./|
|     U     |
|____% %____|

Diagram 1

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---

Setup 2

balls:8B-8R; start:B; trace:b|rB

Solution 2

 ___o    ___
|  .\. ./.  |
| .-.\./.-. |
|.-.-.^.-.-.|
|-.-././.-.-|
|.-.\.^.-.-.|
|-.-.\./.-.-|
|.-.-.X.-.-.|
|-.-.\./.-.-|
|.-.-.X.-.-.|
|-.-.\.\.-.-|
|     U     |
|____% %____|

Diagram 2

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Challenge #21: Quantum Number

Objective

Use register A to count the number of blue balls. Use 15 or fewer balls.

Setup

balls:15B-0R; start:B; trace:15B

 ___o    ___
|  .<. .-.  |
| .\.\.-.-. |
|.-.<./.-.-.|
|-.\.\.-.-.-|
|.-.<./.-.-.|
|-.\.\.-.-.-|
|.-.<./.-.-.|
|-.\.\.-.-.-|
|.-.\./.-.-.|
|-.-.\.-.-.-|
|     /     |
|____% %____|

Diagram

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Challenge #22: Depletion

Objective

Register A starts at 15. Subtract the number of blue balls from the register. (Use 15 or fewer balls.)

Setup

balls:15B 0R; start:B; trace:15B

Solution

 ___o    ___
|  .>. .-.  |
| ././.-.-. |
|.\.>.-.-.-.|
|-././.-.-.-|
|.\.>.-.-.-.|
|-././.-.-.-|
|.\.>.-.-.-.|
|-././.-.-.-|
|.\./.-.-.-.|
|-./.-.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #23: Tetrad

Objective

Let exactly 4 blue balls reach the end. (Intercept the 5th.)

Setup

balls:8B-8R; start:B; trace:b4B

Solution

 ___o    ___
|  .<. .-.  |
| ././.-.-. |
|.\.<.-.-.-.|
|-././.-.-.-|
|.\.>.-.-.-.|
|-./.U.-.-.-|
|.\.-.-.-.-.|
|-./.-.-.-.-|
|.\.-.-.-.-.|
|-./.-.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #24: Ennead

Objective

Let exactly 9 blue balls reach the end. (Intercept the 10th.)

Setup

balls:12B 12R; start:B; trace:b9B

Solution

 ___o    ___
|  .>. .-.  |
| ././.-.-. |
|.\.<.-.-.-.|
|-././.-.-.-|
|.\.<.-.-.-.|
|-././.-.-.-|
|.\.>.-.-.-.|
|-./.U.-.-.-|
|.\.-.-.-.-.|
|-./.-.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #25: Regular Expression

Objective

Generate the pattern 3R6B.

Setup

balls:8B-8R; start:B; trace:r3R6B

Solution

 ___o    ___
|  .>. .>.  |
| ././././. |
|.\.<.\.>.-.|
|-./././.U.-|
|.\.>./.-.-.|
|-./.\.-.-.-|
|.\.-.\.-.-.|
|-./.-.\.-.-|
|.\.-.-.\.-.|
|-./.-.-.\.-|
|     -     |
|____% %____|

Diagram

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Challenge #26: Nucleus

Objective

Generate the pattern 4B1R4B.

Setup

balls:10B-10R; start:B; trace:r4B1R4B

Solution

 ___o    ___
|  .>. .>.  |
| ./././.U. |
|.\.>./.-.-.|
|-./.X.-.-.-|
|.\./.\.-.-.|
|-./.-.\.-.-|
|.\.-.-./.-.|
|-./.-.\.-.-|
|.\.-.-./.-.|
|-./.-.\.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #27: Reflection

Objective

Reverse the direction of each of the 9 starting bits, regardless of the direction they point to start

Setup

balls:8B-8R; start:B; trace:rBB

Solution

 ___o   o___
|  .>. .\.  |
| .^.\.-.^. |
|.\./.^.\./.|
|-.^.\./.U.-|
|.\./.^.-.-.|
|-.^.\./.-.-|
|.\./.^.-.-.|
|-.^.\./.-.-|
|.\./.^.-.-.|
|-./.\./.-.-|
|     \     |
|____% %____|

Diagram

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Challenge #28: Latch

Objective

Release only the blue balls.

Setup

balls:8B-8R; start:B; trace:8B

Solution

 ___o    ___
|  .\. .-.  |
| .-.\.-.-. |
|.-.-.}.-.-.|
|-.-.}*-.-.-|
|.-.-./.-.-.|
|-.-./.-.-.-|
|.-.\.-.-.-.|
|-.-./.-.-.-|
|.-.\.-.-.-.|
|-.-./.-.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #29: One-Shot Switch

Objective

Release a blue ball, a red ball, and then the rest of the blue balls.

Setup

balls:8B-8R; start:B; trace:7BRB

Solution

 ___o    ___
|  .{. ./.  |
| .{*\./.-. |
|.-.\.X.-.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|.-.\.-./.-.|
|-.-./.\.-.-|
|     -     |
|____% %____|

Diagram

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Challenge #30: Overflow

Objective

Count the blue balls in register A. If there are more than 7, gear bit OV must flip right (and stay right) to indicate the overflow.

Setup

balls:*B-0R; start:B; trace:*B

Solution

 ___o    ___
|  .<. .-.  |
| .\.\.-.-. |
|.-.<./.-.-.|
|-.\.\.-.-.-|
|.-.<./.-.-.|
|-*{./.-.-.-|OV
|.{./.-.-.-.|
|\./.-.-.-.-|
|./.-.-.-.-.|
|\.-.-.-.-.-|
|     -     |
|____% %____|

Diagram

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