Random Puzzles 

Workings

Hint
What can digits 4 and 5 be?

Answer
71842.

Reasoning
The number can be represented as:

   - - - - -

By (5), Digit 5 is half of Digit 4, so we have four possibilities:

   - - - 2 1
   - - - 4 2
   - - - 6 3
   - - - 8 4

By (4), Digit 1 is higher than the sum of Digit 4 and Digit 5, so we can eliminate two possibilities, leaving:

   - - - 2 1
   - - - 4 2

By (7), Digit 5 is between Digit 2 and Digit 1, so we can eliminate - - - 2 1, leaving:

   - - - 4 2

By (4), Digit 1 must be higher than the sum of Digit 4 and Digit 5, so we have three possibilities:

   7 - - 4 2
   8 - - 4 2
   9 - - 4 2

By (6), Digit 1 is 1 smaller than Digit 3 we can eliminate 9 - - 4 2, and fill in Digit 3, leaving:

   7 - 8 4 2
   8 - 9 4 2

By (3), Digit 2 is the lowest digit, and must be 1:

   7 1 8 4 2
   8 1 9 4 2

By (1), the only possibility is:

   7 1 8 4 2

Workings

Hint
Jesse is the oldest.

Answer
Morgan is 3 and has two teddies.
Pat is 1 and has one teddies.
Jesse is 4 and has three teddies.
Dale is 2 and has four teddies.

Workings

Hint
Think of the pages from 1-9, and then 10-99.

Answers
There are 147 pages. The number 3 appears 35 times.
Answer #1
For pages 1-9, there are 9 pages, which is 9 digits.

For pages 10-99, there are 90 pages, which is 180 digits.

This is a total so far of 189, therefore we require another 333 – 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.

Taking us to 9 + 90 + 48 = 147 pages in total.

Answer #2
From page 1 to 147 we have 15 pages that end in 3:

   3, 13, 23, ..., 143

We also have the ten pages that start with 30:

   30, 31, 32, ..., 39

Plus the ten pages that start with 130:

   130, 131, 132, ..., 139

For a total of 15 + 10 + 10 = 35 number 3's.

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 2^nd in croquet.
Name    Age    Chess  Croquet
Dale
Emery
Frankie               2
Glen

By (2), Dale came 3^rd 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 4^th in chess, came 3^rd in croquet, and by (7), they are 19. This can't be Dale (3^rd in chess), or Frankie (2^nd 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 4^th in croquet, so must be 1^st. Leaving Emery in 4^th.
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 4^th in both (as Glen is already 4^th in chess), so must be Frank, 2^nd in both. Leaving Emery 1^st 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