Puzzle 589
If I buy a melon and a coconut, the cost will be £1.19.
If I buy a melon and a pineapple, the cost will be £1.45.
If I buy a coconut and a pineapple, the cost will be £1.40.
What are the individual prices?
Puzzle Copyright © Kevin Stone
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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).
Puzzle 590
At a recent motorsport gathering, four proud owners were grouped together around the blue Ferrari, discussing their gleaming sports cars.
Alex was overheard bragging about their brand new silver Mercedes.
The person whose surname was Smith went to great lengths to explain to Blake, the virtues of their blue Ferrari.
The person whose surname was Wilshaw and Dale occasionally made eye contact.
The person whose surname was Richards showed everyone a recent photo of their red Rolls Royce.
The person whose surname was Stone listened intently while Charlie went on about their green Corvette.
Who owns which car?
Puzzle Copyright © Kevin Stone
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Hint
One of the owners was Alex Stone.
Answer
Alex Stone owns the silver Mercedes.
Blake Richards owns the red Rolls Royce.
Charlie Wilshaw owns the green Corvette.
Dale Smith owns the blue Ferrari.
Puzzle 591
If Malcolm, Laura, John, Alan, Brenda and Kevin like chocolate...
...and Norman, Steve, Thomas, Zebedee do not...
...does Peter like chocolate?
Puzzle Copyright © Kevin Stone
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Hint
Think about the alphabet.
Answer
No.
Only people with initials A-M do like chocolate, others do not.
Puzzle 592
This equation contains the numbers 1-8.
Can you complete it?
6.
.. x
————
....
Puzzle Copyright © Kevin Stone
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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.
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