Brain Teasers and Puzzles 

Workings

Hint
A little algebra might help.

Answer
Pineapple = 83p, coconut = 57p, melon = 62p.

Reasoning
If we assign the letters P, C and M to the fruits, and work in pence we have:

(1)   M + C = 119
(2)   M + P = 145
(3)   C + P = 140

Using (2) – (1) we have:

(4)   P – C = 26

And (3) + (4) gives:

         2P = 166
          P = 83

This can then be substituted back into (2) and (3).

Workings

Hint
What colour was the Stellar?

Answer
Dale Smith owned the blue Lunar.

Billie Richards owned the red Orbital.

Charlie Wilshaw owned the green Galactic.

Alex Stone owned the silver Stellar.

Reasoning
By (2) the Lunar was Blue, and was owned by Mr Smith.

By (4) the Orbital was Red, and was owned by Mr Richards.

By (5) the Galactic was Green, and was owned by Charlie.

Therefore the Stellar was silver, and by (1) was owned by Alex.
           Smith    Blue   Lunar
           Richards Red    Orbital
   Charlie          Green  Galactic
   Alex             Silver Stellar

By (2), Mr Smith wasn't called Billie, so it must have been Billie Richards, and Dale Smith.

By (5) Mr Stone wasn't called Charlie, so it must have been Charlie Wilshaw, and Alex Stone.
   Dale    Smith    Blue   Lunar
   Billie  Richards Red    Orbital
   Charlie Wilshaw  Green  Galactic
   Alex    Stone    Silver Stellar

Workings

Hint
Think about the alphabet.

Answer
No.

Only people with initials A-M do like chocolate, others do not.

Workings

Hint
The answer begins with 3.

Answer
64 x 58 = 3712.

Reasoning
Since no digit is duplicated, neither number can end in 1, otherwise, the last digit of the answer would already have been used.

Neither number can end in 5 because the answer would then end in 5 or 0.

So the first number can only be 62, 63, 64, 67, or 68.

We can now look at what the second number can end with, and we find that...

   if the first number was 62, the second number can only end in 4 or 7.

Why...
   not 1 as previously explained
   not 2 because we've already used that in the 62
   not 3 because 62 x *3 would end in 6, which is already in the 62
   not 5 as previously explained
   not 6 because we've already used that in the 62
   not 8 because 62 x *8 would end in 6, which is already in the 62

We can repeat this for the other possible first numbers and find that...

   if the first number was 62, the second number can only end in 4 or 7.
   if the first number was 63, the second number can only end in 4, 7, or 8.
   if the first number was 64, the second number can only end in 2, 3, 7, or 8.
   if the first number was 67, the second number can only end in 2, 3, or 4.
   if the first number was 68, the second number can only end in 3 or 4.

Let's check these in turn...

If the first number was 62, the only possible values are:

   62 x 14 = 868
   62 x 34 = 2108
   62 x 54 = 3348
   62 x 74 = 4588

or

   62 x 17 = 1054
   62 x 37 = 2294
   62 x 57 = 3534
   62 x 87 = 5394

Only 4 calculations are required for each option, as we didn't need to check 62 x 84 as we already know that the answer would end in 8, or 62 x 47 as we already know that the answer would end in 4.

All of these answers fail as they don't contain all of the digits.

Similarly, we can look at 63, then 64, etc. For each of the numbers, we have to check the possible endings, but in each case, only 4 calculations are required (as seen in the examples above).

We (quickly?) find 64 x 58 = 3712.