Hard Puzzles

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Puzzle 17

Matthew Shelborn frequently has to travel for his company, which gives him a chance to meet many people from all parts of the USA. In April, Matthew flew to five different US cities on business and he flew a different airline each time. During each trip he chatted with the person next to him, and no two people he talked to were in the same profession.

From the information, can you determine the date Matthew made each flight (each was on a Monday exactly one week apart starting on April 2nd), the airline he flew, his destination, and the profession of the person who sat next to him on each flight?

Three consecutive flights were, in order from first to last, the flight Matthew took with WTA Airways, the flight where he sat next to the teacher, and the flight he took to Atlanta.
Matthew sat beside the sports coach on a flight some time earlier in the month than the one he took to Seattle.
The week he flew Air Express was some time earlier in the month than the trip to Boston, which was some time earlier in the month than the trip where he sat next to the ballet dancer.
It wasn't on the trip to San Diego where Matthew sat next to the doctor.
Matthew didn't fly Skyways on his trip to Seattle, and he didn't fly WTA Airways on the trip where he sat next to the sports coach.
Atlanta was not Matthew's destination on the trip where he made the acquaintance of the ballet dancer.
The Fly America flight was exactly two weeks before the flight where Matthew passed the time chatting with the attorney. Dates       : April 2nd, April 9th, April 16th, April 23rd, April 30th
Airline     : Air Express, Fly America, MidUSA Air, Skyways, WTA Airways
Destination : Atlanta, Boston, Chicago, San Diego, Seattle
Seat Mate   : Attorney, Ballet Dancer, Doctor, Sports Coach, Teacher

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Answer
Date        Airline      Destination  Seat Mate
April 2nd   WTA Airways  Chicago      Doctor
April 9th   Fly America  San Diego    Teacher
April 16th  Air Express  Atlanta      Sports Coach
April 23rd  Skyways      Boston       Attorney
April 30th  MidUSA Air   Seattle      Ballet Dancer

The trip to Atlanta (1), the trip where Matthew sat next to the ballet dancer (3), and the trip where Matthew sat next to the attorney (7) were among the last three trips [April 16th, 23rd, and 30th (intro)], and the trip to Atlanta wasn't the one where he met the ballet dancer (6) or the attorney [he flew WTA Airways exactly two weeks before the one to Atlanta, and he flew Fly America exactly two weeks before he sat by the attorney (7), so, these three are separate flights, in some order.

He didn't sit by the teacher on the trip to Atlanta (1), so the flight were he sat by the teacher was on one of the first two flights [April 2nd and April 9th (intro)], but it wasn't first [after WTA Airways](1), therefore, April 2nd flight was the WTA Airways flight, the one where he sat by the teacher was the April 9th flight, and the one to Atlanta was the April 16th flight, and he sat by the ballet dancer and attorney on the April 23rd and April 30th flight, in some order.

He didn't sit beside the sports coach on the WTA Airways flight (5) so that wasn't April 2nd, he sat beside the sports coach on the Atlanta flight [April 16th] and it was the April 2nd flight where he sat next to the doctor.

April 2nd [first flight, WTA Airways, doctor] wasn't to Seattle (2), Boston (3), or San Diego (4), that flight was to Chicago.

The April 9th flight wasn't to Seattle [after sports coach which was April 16th] or to Boston [after Air Express, which would have to be April 2nd, but WTA Airways was April 2nd (1)](3), so, on April 9th he flew to San Diego.

Boston wasn't the last destination (3), so it was his destination on April 23rd and Seattle was his destination on April 30th.

Boston [April 23rd] was before the one where he sat by the ballet dancer (3), so he sat by the ballet dancer on April 30th flight to Seattle, and it was on the April 23rd flight to Boston that he sat by the attorney.

Since he sat by the attorney on the April 23rd flight, then he flew Fly America on the 9th [exactly two weeks before](7).

He flew Air Express before the flight when he flew to Boston [April 23rd](3) so he flew Air Express on the 16th.

He didn't fly Skyways to Seattle [April 30th](5), so, he flew Skyways to Boston on the 23rd and his last flight that month was on MidUSA Air (intro).

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Puzzle 18

During the recent BrainBashers cipher convention, a binary code contest took place.

The contest consisted of a binary code transmission where the spaces between the letters were missing and there was no punctuation.

Each letter of the alphabet was translated into its binary equivalent based on its position in the alphabet. The resulting code was then blocked in groups of five digits.
a=1, b=10, c=11, d=100, e=101, f=110, g=111, h=1000, i=1001, j=1010, k=1011, l=1100, m=1101, n=1110, o=1111, p=10000, q=10001, r=10010, s=10011, t=10100, u=10101, v=10110, w=10111, x=11000, y=11001, z=11010

What is the answer to the question being asked?
11001 11010 01000 10011 00111 00110 01111 01101 01100 10110 01100 10011 10110 10011 11010 11100 10100 10000 10101 11010 11010 11001 01100 11010 01000 11111 01011 11100 01010 01001 10100 10111 11111 01011 10010 01000 10111 00100 00100 11101 00111 00111 01110 11001 10011 10011 10110 00011 00101 10001 10101 10110 01110 10010 01111 11110 10111 10001 10100 10011 00111 11111 10101 10000 11001 01011 00111 11111 10101

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Puzzle 19

What four related words are merged here:
SWAS PURI UINM NTTU MGER MNER

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Puzzle 20

In this long division, each number has been replaced by another. The answer has also been removed. Can you determine the answer?
       ....
    ———————
75 | 796767
     791
      ——
       57
       30
       ——
        86
        82
        ——
         47
         47
         ——
          9

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