Random 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
A tricky base 8 question.

Answer
61.

Each term is a square expressed in base eight, 7 2=49 = 61 in base 8.

Workings

Hint
Mary's name is Dancer.

Answer
Louise Archer will make the chocolate cake.
Julie Bowness will make the coffee cake.
Kay Cook will make the plain cake.
Mary Dancer will make the vanilla cake.

Workings

Hint
What could we do with the digits?

Answer
If the sum of the digits is divisible by nine, so is the number.

Add up all of the digits in the number and see if the sum is divisible by 9. If you still can't tell, you can add those digits again to see if the new sum is divisible by 9. You can keep going until you the sum is obviously divisible by 9 or not.

For example, is 486451464 divisible by 9?

Do 4 + 8 + 6 + 4 + 5 + 1 + 4 + 6 + 4 = 42.

Is 42 divisible by 9? Not sure, you can then do:

4 + 2 = 6. Which clearly isn't divisible by 9. So our original number, 486451464, isn't either.