Brain Teasers and Puzzles 

Workings

Hint
The 2^nd word begins with the letter B.

Answers
a-a-e = amaze (MZ) --ave = brave (BR) -uie- = quiet (QT) --gon = wagon (WA) p--ot = pivot (IV) vi-e- = vixen (XN) -ac-t = yacht (YH) --met = comet (CO) b--ep = bleep (LE) -u-ge = judge (JD) -lan- = flank (FK) -ra-e = grape (GP) bon-- = bonus (US)
This puzzle isn't guaranteed to have a unique answer, can you find another?

Workings

Hint
Try to find Drew's boat colours first.

Answer
Alex      Red     + Green
Billie    Green   + Blue
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Reasoning
By (3), Yellow and Blue went together (Combination1: Yellow + Blue).

By (4), Green and Blue went together (Combination2: Green + Blue).

By (2), Billie had Green. By (5), Charlie had Yellow. By (6), Drew had Blue. Giving:
Alex
Billie    Green
Charlie   Yellow
Drew      Blue

By (6), Drew had Blue, but not Green. This can't have been (Combination2: Green + Blue), so must have been (Combination1: Yellow + Blue):
Alex
Billie    Green
Charlie   Yellow
Drew      Blue    + Yellow

By (2), Billie didn't have Red, so Alex and Charlie must have had Red:
Alex      Red
Billie    Green
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Which means that Billie had (Combination2: Green + Blue), and Alex had Green:
Alex      Red     + Green
Billie    Green   + Blue
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Workings

Hint
The number is less than 20.

Answer
8.

Reasoning
We need a number (N) such that:

2 x N = 14 + N
             —
             4

Multiply throughout by 4 to give:

8 x N = 56 + N

So:

7 x N = 56

So N = 8.

Double-Checking
Its double is 16.

Its quarter is 2.

So its double is fourteen more than its quarter.

Workings

Hint
The words are linked by their letters.

Answer
Approved.

The initial letters spell ORANGE and the last letters spell INDIGO.