BrainBashers - Hard Puzzles

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Puzzle 9

Your objective is to place some diagonal mirrors into the grid.

If a ray of light is shone in to the grid from each of the letters, and allowed to bounce off the internal diagonal mirrors, each will exit the grid at the twin of the letter that it entered the grid. For example, a ray entering at either letter D will bounce off some mirrors and exit the grid at the other letter D.

Each row and each column will contain exactly two of the diagonal mirrors.

Puzzle Copyright © Elliott Line
This puzzle appeared in Mensa's EnigmaSig (196.26) and is used with permission.

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Puzzle 10

Complete the grid such that every row and column contains the digits 1 to 6.

All squares that are connected contain the same digit.

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Puzzle 11

Fill in the missing numbers with the digits 1 to 9. A diamond shape in the middle means that the four numbers around it add to 20.

Each uses a different way to add to 20, if there is already 1 + 3 + 7 + 9, then there will not be another using the digits 1, 3, 7 and 9 (in any order).

The same digit isn't allowed to touch, even diagonally.

Puzzle Copyright © Elliott Line
This puzzle appeared in Mensa's EnigmaSig (195.08) and is used with permission.

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Puzzle 12

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 2^nd), 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 2^nd, April 9^th, April 16^th, April 23^rd, April 30^th
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 2^nd   WTA Airways  Chicago      Doctor
April 9^th   Fly America  San Diego    Teacher
April 16^th  Air Express  Atlanta      Sports Coach
April 23^rd  Skyways      Boston       Attorney
April 30^th  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 16^th, 23^rd, and 30^th (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 2^nd and April 9^th (intro)], but it wasn't first [after WTA Airways](1), therefore, April 2^nd flight was the WTA Airways flight, the one where he sat by the teacher was the April 9^th flight, and the one to Atlanta was the April 16^th flight, and he sat by the ballet dancer and attorney on the April 23^rd and April 30^th flight, in some order.

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

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

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

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

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

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

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

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

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