## March 2015 Logic & Maths Problems – Solutions

If John is lying, then George and Ringo would be telling the truth, which would mean John was not lying, so he can’t be the liar.
If Paul was lying, then Ringo would also be lying, so he must be telling the truth, as well.
So we now know that neither John nor Paul finished last. If Ringo was lying, then George would have finished last, which would mean that he was lying, as well. So Ringo can’t be lying.
This leaves George as our liar, so we know George did not finish first. Neither did Ringo (he finished last), nor did John (he finished neither first nor last). Therefore, Paul won the race!

2. Four minutes

3. 8:02 or 2 minutes past 8.

IF my house number was a multiple of 3, it would have to be 51, 54 or 57.
51, 54, and 57 are NOT multiples of 4.
But if my house number is NOT a multiple of 4, the answer has to lie between 60 and 69.
So my house number is NOT a multiple of 3.
My house number can’t be a multiple of 6 either, because any multiple of 6 is also a multiple of 3.
So, because my house number is NOT a multiple of 6, it must lie between 70 and 79.
If my house number is NOT a multiple of 4, it lies in the range 60 to 69.
The only possibility is that my house number IS a multiple of 4, lies in the range 70 to 79, but is NOT also a multiple of 3 (or 6).
The only candidate is 76.

5. 26

6. Tuesday

7. Incorrectly (Pointer moves down during a flood)

8. 34

9. 4 animals

10. Green