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
The sequence involves both adding and multiplying in some way.

Answer
153.

The sequence is created using: +1 x1 +2 x2 +3 x3 +4 x4 +5.

Workings

Hint
Can the fractions be simplified?

Answer
667.

Reasoning
3      8      1
—  of  —  of  —  of 2001
4      9      2

which simplifies to:
24
——  of 2001
72

which simplifies to:
1
—  of 2001
3

Giving 667.

Workings

Hint
How old was the person in second place?

Answer
# Name    Age
1 Drew    30
2 Emery   24
3 Glen    27
4 Alex    32

Reasoning
By (2), because Glen was three years older, the person in 2^nd place was either 24 or 27.

But 2^nd place can't have been 27, because, by (4), Emery was ahead, but didn't win.

So 2^nd place was 24, and Glen was 27.

By (3), Drew could only be 27 or 30, but we now know what Glen was 27, so Drew was 30.

By (1), the person who came last was 32:
1
2         24
3
4         32

By (4), the 27-year-old can't have won,
1 Drew    30
2         24
3 Glen    27
4         32

By (4), Emery beat the 27-year-old:
1 Drew    30
2 Emery   24
3 Glen    27
4         32

Leaving Alex in last place.
1 Drew    30
2 Emery   24
3 Glen    27
4 Alex    32