Puzzle 5
School Reunion '62 – Logic Puzzles
During a recent school reunion, four friends were discussing their starting salaries.
The salaries in question were, 8, 10, 12 and 14 thousand pounds per year.
The MP earned the most.
Alex earned more than Billie and the doctor earned more than Drew, the vet.
Billie, the lawyer, did not start on £10,000 nor did Drew.
And Chris couldn't remember.
Can you determine who has which job and their starting salaries?
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Answer
Name Profession Salary
Alex MP £14,000
Billie lawyer £12,000
Chris doctor £10,000
Drew vet £ 8,000
Puzzle 6
What is the smallest positive integer which, when multiplied by 7, gives an answer consisting of only 4's?
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Hint
It will take a while to check 1 x 7, 2 x 7, 3 x 7. What do we know about the answer?
Answer
63,492 x 7 = 444,444
Reasoning
We can work backwards, as we know that the number multiplied by 7 has only 4's. We can try the following:
4 ÷ 7 ≈ 0.57 x
44 ÷ 7 ≈ 6.29 x
444 ÷ 7 ≈ 63.43 x
4,444 ÷ 7 ≈ 634.86 x
44,444 ÷ 7 ≈ 6,349.14 x
444,444 ÷ 7 = 63,492
Puzzle 7
If I give you seven apples, you will then have five times as many as I would then have.
However, if you give me seven apples, we will then both have the same number of apples.
How many apples do I currently have?
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Hint
A little bit of algebra might help.
Answer
I have 14 apples and you have 28 apples.
Reasoning
We can work this out with a little algebra. I have A apples and you have B apples, then
[1] 5 x (A – 7) = B + 7
[2] A + 7 = B – 7
From [1] we have:
5A – 35 = B + 7
[3] 5A = B + 42
From [2] we have:
[4] A + 14 = B
We can then use [4] in [3] to give:
5A = (A + 14) + 42
5A = A + 56
4A = 56
A = 14
Which gives B = 28 (by [4]).
Puzzle 8
If you turn a right handed glove inside out …
… which hand will it now fit?
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Hint
Perhaps think about the thumb?
Answer
It will now fit the left hand.
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