## People Mover

by Nina Hinrichs, Linda Holman

Answer: CAROLE KING

Teams can first solve the logic puzzle to get the 10 stops in order, which read GETFITWALK.
This refers to the GetFit program at MIT, which hosts walks in the MIT tunnel system with stops
labelled with plaques at
the locations marked on the linked map.
Teams should visit the stops in order (stop 1 =
G, stop 2 = E, etc) and overlay the given squares on top of the GetFit plaques. The numbered
circles will appear on top of a letter on each plaque. Reading these letters in number order
gives the message `SHE FELT THE EARTH MOVE`. This refers to the song "I Feel the Earth Move
(Under My Feet)" by Carole King, so the answer is **CAROLE KING**.

## Logic puzzle solution

There are 3 types of constraints in the logic puzzle:

- Global constraints on the entire set of letters, such as the sum of Scrabble score
- Constraints which give subsets of letters, such as exactly 5 ascenders
- Constraints on ordering

One solution method is to use constraints (1) to narrow down the subsets (2), and then apply an ordering (3). Here is a possible solution path:

There are two main global constraints: The total Scrabble score (S.) is 21 and the Morse code representation has 24 symbols. Listing out letters and values for these:

S. | Morse | S. | Morse | S. | Morse | S. | Morse | ||||
---|---|---|---|---|---|---|---|---|---|---|---|

A | 1 | 2 | H | 4 | 4 | O | 1 | 3 | V | 4 | 4 |

B | 3 | 4 | I | 1 | 2 | P | 3 | 4 | W | 4 | 3 |

C | 3 | 4 | J | 8 | 4 | Q | 10 | 4 | X | 8 | 4 |

D | 2 | 3 | K | 5 | 3 | R | 1 | 3 | Y | 4 | 4 |

E | 1 | 1 | L | 1 | 4 | S | 1 | 3 | Z | 10 | 4 |

F | 4 | 4 | M | 3 | 2 | T | 1 | 1 | |||

G | 2 | 3 | N | 1 | 2 | U | 1 | 3 |

Subset constraints include:

(A) Braille—One stop from {U, V, W, X, Y, Z}

(B) Ascender—Five stops from {B, D, F, H, K, L, T}

(C) Morse—There are no {J, H, O} since these have 3 dashes or 4 dots

(D) Semaphore—Five stops from {A, G, H, O, T, W, Z}

(E) NATO—Two stops from {C, F, J, U, W}

Because at most one letter is duplicated, the ascenders must have Scrabble value at least 8, so the remaining 5 non-ascenders have score at most 13. Therefore, none of them can have value 10 (eliminate Q and Z).

The potential list of semaphore letters is now {A, G, T, W}, which means each appears at least once, and one appears twice.

From braille, since the W appears, the {U, V, X, Y} do not appear. Additionally, the W appears exactly once.

If the A or G appeared twice, the total number of Morse symbols from {A, A, G, T, W} or {A, G, G, T, W} would be 11 or 12. There would need to be 4 more unique ascenders from the set {B, D, F, K, L}, which would have value at least 14, leading to a total Morse symbol count of over 24. Therefore, T is the duplicated letter.

The known letter set is {A, G, T, T, W}, with total Scrabble score of 9 and Morse symbol length of
10. The remaining 5 letters are unique and have total Scrabble score of 12 and Morse symbol
length of 14. The other constraints are:

(A) Braille—No {U, V, X, Y, Z}

(B) Ascender—Three stops from {B, D, F, K, L}

(C) Morse—No {J, H, O}

(D) Semaphore—Complete

(E) NATO—One stop from {C, F}

The three stops from {B, D, F, K, L} have morse symbol length of at least 10. If the NATO letter were C, then the total morse symbol count would be too high, so there must be an F in the answer.

We need two more stops from {B, D, K, L} and those, along with two more letters, will have a total Scrabble score of 8 and a Morse symbol length of 10. We enumerate the choices below.

Letter combo | Scrabble score | Morse length | Other two letters |
---|---|---|---|

B, D | 5 | 7 | |

B, K | 8 | 7 | NONE - the Scrabble score is too high |

B, L | 4 | 8 | NONE - the Morse length is too high |

D, K | 7 | 6 | NONE - the Scrabble score is too high |

D, L | 3 | 7 | |

K, L | 6 | 7 |

The three choices that remain all have Morse length of 3 remaining for the last two letters. This must be made up of an E and one of {I, M, N}. The possible Scrabble values for these two letters are 2 or 4, so the two ascenders must be {K, L} and the two remaining letters are E and {I, N}.

The set of 10 letters is {A, E, F, G, K, L, T, T, W} and {I, N}.

We can now start putting them in order.

- The duplicate letter, T, goes in stops 3 and 6
- Stop 9 is an ascender {F, K, L}
- Stops 1 and 8 are acute semaphore letters {A, G, W}
- The highest scoring Scrabble letter, K, goes in stop 10
- The NATO letters, F and W go in spots 4 and 7. Since stops 4 through 7 are in alphabetical order, the F is in spot 4 and the W is in spot 7

1 A or G

2 E or {I,N}

3 T

4 F

5 E or {I,N}

6 T

7 W

8 A or G

9 L

10 K

We can now use the Morse code pattern to deduce the final ordering—the G cannot follow the W or there will be four dashes in a row. Stops 4 through 7 are in alphabetical order, so stop 5 must be the I or N, leaving stop 2 as the E. There must be a place with three dots in a row, so the last letter in stop 5 is an I.

The final stop order is GETFITWALK.