Brain Teasers and Puzzles 

Workings

Hint
How old could Glen be?

Answer
Name    Age    Chess  Croquet
Dale    15     3      1
Emery   16     1      4
Frankie 18     2      2
Glen    19     4      3

Reasoning
The possible ages are: 15, 16, 18, 19.

Breaking the clues down, and numbering them:
Frankie beat Glen in chess. Dale came third (chess). The 16-year-old won (chess). Frankie came second in croquet. The 15-year-old won (croquet). Dale beat the 18-year-old (croquet). The 19-year-old came third (croquet). Emery is 3 years younger than Glen. The person who came last in chess came third in croquet. Only one person got the same position in both games.
By (4), Frankie came 2nd in croquet.
Name    Age    Chess  Croquet
Dale
Emery
Frankie               2
Glen

By (2), Dale came 3rd in chess.
Name    Age    Chess  Croquet
Dale           3
Emery
Frankie               2
Glen

By (8), Emery is 15 or 16, and Glen is 18 or 19.

By (9), the person who came 4th in chess, came 3rd in croquet, and by (7), they are 19. This can't be Dale (3rd in chess), or Frankie (2nd in croquet), or Emery (aged 15 or 16), so it must be Glen.
Name    Age    Chess  Croquet
Dale           3
Emery
Frankie               2
Glen    19     4      3

By (6), Dale can't have been 4th in croquet, so must be 1st. Leaving Emery in 4th.
Name    Age    Chess  Croquet
Dale           3      1
Emery                 4
Frankie               2
Glen    19     4      3

By (10), only one person got the same position in both games, this can't be Emery 4th in both (as Glen is already 4th in chess), so must be Frank, 2nd in both. Leaving Emery 1st in chess.
Name    Age    Chess  Croquet
Dale           3      1
Emery          1      4
Frankie        2      2
Glen    19     4      3

By (3) and (5) we know the ages of the winners in each competition, and Frankie is therefore 18.
Name    Age    Chess  Croquet
Dale    15     3      1
Emery   16     1      4
Frankie 18     2      2
Glen    19     4      3

Workings

Hint
Find anagrams of the words in this order: PLEASE, TRANCE, LISTEN, WARNED, VEINED, BRUISE.

Answers
ANSWER.

Reasoning
The initial letters are RWASEN, which is an anagram of ANSWER.
bruise becomes rubies warned becomes wander please becomes asleep listen becomes silent veined becomes envied trance becomes nectar

Workings

Hint
What letters are missing?

Answer
The letter was written on a typewriter that has a problem with the top row of letters – they did not print correctly. The letter should have read:

Dear Kevin,

I would like to complain about the top row of my typewriter.

These letters do not appear to be working correctly.

As you can see, they are missing from this document.

I would be very grateful if you could correct this problem immediately.

Kind regards.

Sam South.

Workings

Hint
Think outside the box.

Answer
Start from the top left dot, and go past the top right dot, and then diagonally down to the bottom left dot, back up to the top left dot, and diagonally down to the bottom right dot.