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Puzzle 453
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.
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, and this doesn't work.
Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36, and this doesn't work.
Let's try 3 x 315 + 1: 946 ÷ 11 = 86, and this works, and is the answer.
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Puzzle 454
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?
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
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
