Puzzle 217
My local greengrocer is a would-be mathematician.
She likes to arrange the apples in nice rows.
When she lays the apples in rows of 3, she has one left over.
And, when she lays them in rows of 5, she also has one left over.
Remarkably, she also has one left over when she arranges them in rows of 7 and 9.
But 11 seems to be the magic number, because in rows of 11 there are no apples left over.
How many apples does she have?
Puzzle Copyright © Kevin Stone
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Hint
There are fewer than 1,000 apples.
Answer
946 apples.
Reasoning
We know that (answer – 1) is divisible by 3, 5, 7, and 9.
If it's divisible by 9 then it's automatically divisible by 3.
So the number must be a multiple of 5, 7, and 9.
[5 x 7 x 9 = 315]
Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+1).
Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73 – this doesn't work.
Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36 – this doesn't work.
Let's try 3 x 315 + 1: 946 ÷ 11 = 86 – this works and is the answer.
Puzzle 218
The local River Trent is 4,100 inches wide, which happens to be a fantastic number.
There is a magnificent, perfectly straight, bridge that spans the river at right angles.
During a recent survey of the area, it was found that one-seventh of the overall length of the bridge was on one bank of the river, and one-eighth of the bridge was on the other bank.
What is the total length of the bridge that spans the River Trent?
Puzzle Copyright © Kevin Stone
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Hint
What fraction of the length of the bridge is on the banks?
Answer
5,600 inches.
Reasoning
We know that 1/7 + 1/8 of the total length is on the banks of the river, and 1/7 + 1/8 = 15/56.
So the river width (4,100 inches) is the remaining 41/56 of the bridge.
Therefore:
41/56 x length = 4100
So:
length = 4100 x 56/41
length = 5600
As required.
Puzzle 219
Trade Convention #1 - Logic Puzzles
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?
Puzzle Copyright © Kevin Stone
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Hint
Find out who used to be the teacher first.
Answer
Billie Baker – plumber + carpenter
Eddie Teacher – carpenter + plumber
Charlie Carpenter – baker + teacher
Davie Plumber – teacher + baker
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 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 220
Last week my wife and I found ourselves stranded on an island, oops!
Unfortunately, we were also stranded with our two sons, with no clear means of rescue.
Luckily, I came across an old rickety boat which I knew could carry either one adult or two children.
How did I rescue my family?
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Hint
The sons row across first.
Answer
The two sons rowed to safety first, one son rowed back.
I rowed to safety and the other son rowed back to the island.
The two sons rowed to safety first, one son rowed back again.
My wife rowed to safety and the other son rowed back.
Finally, the two sons rowed to safety.
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