Workers with the surnames Baker, Teacher, Carpenter, and Plumber are currently attending an annual convention.
No-one is currently, nor has ever been, in the same occupation as their name, and no-one has had the same occupation twice. Charlie has never been a carpenter, and Mr Teacher is now a plumber. Davie used to be a teacher, but Mr Billie Baker never has. Mr Plumber is not called Eddie, and Mr Carpenter wasn't previously a teacher. The previous occupations were all different, and the current occupations are all different.
Can you determine the full names of each of the attendees, along with their current and previous occupation?
The previous occupation is followed by the current.
Reasoning
The four forenames are: Billie, Charlie, Davie, Eddie.
The four surnames are: Baker, Teacher, Carpenter, Plumber
The four occupations are: baker, teacher, carpenter, plumber.
By (3), we have Billie Baker:
Billie Baker – ? + ?
Teacher – ? + ?
Carpenter – ? + ?
Plumber – ? + ?
By (2), Mr Teacher is currently a plumber:
Billie Baker – ? + ?
Teacher – ? + plumber
Carpenter – ? + ?
Plumber – ? + ?
By (3) Mr Baker was not previously a teacher. By (4), neither was Mr Carpenter. And by (1) Mr Teacher can't have been either. Therefore, Mr Plumber used to be a teacher, and is called Davie:
Billie Baker – ? + ?
Teacher – ? + plumber
Carpenter – ? + ?
Davie Plumber – teacher + ?
By (3), Mr Baker has never been a teacher, and by (1), Mr Plumber can't currently be a teacher either. Also, by (1), neither can Mr Teacher. Therefore, Mr Carpenter must currently be a teacher:
Billie Baker – ? + ?
Teacher – ? + plumber
Carpenter – ? + teacher
Davie Plumber – teacher + ?
By (1), Mr Baker can't be a baker, so only Mr Plumber can currently be a baker. Leaving Mr Baker as a carpenter currently:
Billie Baker – ? + carpenter
Teacher – ? + plumber
Carpenter – ? + teacher
Davie Plumber – teacher + baker
By (1), only Mr Teacher could have previously been a carpenter:
Billie Baker – ? + carpenter
Teacher – carpenter + plumber
Carpenter – ? + teacher
Davie Plumber – teacher + baker
By (2), Charlie has never been a carpenter, and since Mr Teacher has, Charlie must be Mr Carpenter.
Billie Baker – ? + carpenter
Teacher – carpenter + plumber
Charlie Carpenter – ? + teacher
Davie Plumber – teacher + baker
By (1), we now know all of the occupations, and Eddie must be Mr Teacher:
Billie Baker – plumber + carpenter
Eddie Teacher – carpenter + plumber
Charlie Carpenter – baker + teacher
Davie Plumber – teacher + baker
???
Puzzle 6
A rich aristocrat decided that he would give every man 45 dollars and every woman 60 dollars.
Only one ninth of the men and only one twelfth of the women collected their dues.
Can you tell me how much money the aristocrat spent if there were 3552 people in total?
Hint
It doesn't actually matter how many men or women there were.
Answer
17,760 dollars.
If there were M men, then there were (3552 - M) women.
So one ninth of the men each received 45 dollars and one twelve of the women each received 60 dollars. So the total received was:
= 45 x 1 x M + 60 x 1 x (3552 - M)
— ——
9 12
Simplify the two fractions by dividing the 45 by 9, and the 60 by 12 respectively.
= 5 x M + 5 x (3552 - M)
= 5M + 17760 - 5M
= 17760
?
Puzzle 7
If I was in Florida and dropped a heavy ball into a bucket of water which was at a temperature of 45 °F and dropped another identical ball into an identical bucket of water at a temperature of 25 °F …
… which ball would hit the bottom of the bucket first?
Hint
Remember that the question uses Fahrenheit °F.
Answer
The ball would reach the bottom of the 45 °F bucket first because the water is frozen in the 25 °F bucket!
??
Puzzle 8
At my local farmer's merchant, you can buy chicken feed for 15c per tonne, pig feed for $1.25 per tonne, and cattle feed for 40c per tonne. The feed can only be purchased by the tonne, and part tonnes aren't sold.
Last week I bought some animal feed, and luckily I managed to buy exactly 100 tonnes for exactly $100. How much of each feed did I buy?
Hint
What are the maximum and minimum tonnes of pig feed I could have bought?
Answer
I bought 15 tonnes of chicken feed, 75 tonnes of pig feed, and 10 tonnes of cattle feed.
15 x 0.15 = 2.25 75 x 1.25 = 93.75 10 x 0.40 = 4.00
100 tonnes = $100.00
A possible solution method follows …
I couldn't have bought 80 tonnes of pig feed because this would have cost the full $100.00, but I wouldn't have then had 100 tonnes in total.
Similarly, 70 tonnes of pig feed would have been too few, as this would cost $87.50 and even the remaining 30 tonnes all being cattle feed wouldn't have reached the required $100.00.
So, let's try 71 tonnes of pig feed = $88.75:
plus 1 x chicken feed + 28 x cattle feed is over $100.00 or 2 x chicken feed + 27 x cattle feed is under $100.00
so 71 tonnes of pig feed doesn't work.
Let's try 72 tonnes … and so on.
We soon get to 75 tonnes of pig feed and find the answer.
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