Random Puzzles 

Workings

Hint
There is more than one answer.

Answers
Common words:

hate, late, lane, lone, love
hate, have, hive, live, love
hate, date, dote, dove, love
hate, rate, rote, rove, love
hate, have, wave, wove, love
hate, have, cave, cove, love

Less common words:

hate, late, lave, love
hate, have, hove, love
hate, mate, mote, move, love

Workings

Hint
Break down 210 into its factors.

Answer
12357.

Reasoning
Since 210 = 2 x 3 x 5 x 7, 12357 is the only way to get a 5-digit number, in ascending order.

Workings

Hint
Does the answer change = NO.

Answer
 

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