Brain Teasers and Puzzles 

Workings

Hint
Where does George sit?

Answer
Seat 1 = William
Seat 2 = Nick
Seat 3 = Eric
Seat 4 = Sydney
Seat 5 = George
Seat 6 = Amanda
Seat 7 = Sarah
Seat 8 = Alisa

Reasoning
Sydney is in Seat 4 and is next to George (Clue 6), so George is in either Seat 3 or Seat 5. But George has a higher seat number than Sydney (Clue 7). Therefore, George is in Seat 5.

William is across from George (Clue 2), and therefore is in Seat 1.

William is next to Alisa and Nick (Clue 1), so Alisa and Nick are in Seat 2 and Seat 8 (either way around). But Alisa is not in Seat 2 (Clue 8). Therefore, Alisa is in Seat 8 and Nick is in Seat 2.

Nick is next to Eric (Clue 5) so can only be in Seat 3.

Sarah is across from Eric (Clue 4), and therefore is in Seat 7.

Amanda is next to Sarah (Clue 3) and can only be in Seat 6.

Workings

Hint
The first letters of the words are: W, O, B, H, D, F, C, N, H, D.

Answers
wat + erf + all = waterfall
ove + rbo + ard = overboard
ban + dst + and = bandstand
hai + rbr + ush = hairbrush
dif + fer + ent = different
fis + her + man = fisherman
con + duc + tor = conductor
new + spa + per = newspaper
hea + dli + ght = headlight
dra + gon + fly = dragonfly

Workings

Hint
At each stage, a new dot appears at the top.

Answer
 


Reasoning
At each stage, a new dot starts at the top. The first dot moves clockwise, the second dot moves counter-clockwise, the third dot moves clockwise, etc.

Workings

Hint
If we look at all of the clues, each person appears exactly twice.

Answer
Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.

Reasoning
If we look at all of the clues, each person appears exactly twice.

So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.

So, Alex + Billie + Charlie = 43 years.

In each clue we are given two of the people, so we can use this to find the missing person:

   Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 – 22 = 21 years.

   Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 – 28 = 15 years.

   Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 – 36 = 7 years.

Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:

[1]   A + B = 36
[2]   C + B = 22
[3]   C + A = 28

If we use [3] – [2] we have:

[4]   A – B = 6

If we use [1] + [4] we have:

   2A = 42
    A = 21

By [1] B = 15. By [3] C = 7.