Mathematics puzzle

[pushpinpussy]

for the intellectual ones

four ships left a port at noon January 2 1953

the first ship returns to this port every 4 weeks
the second ship every 8 weeks
the 3rd ship every 12 weeks
the fourth ship every 16 weeks

what date did all four ships meet again at the port.

[Codger]

4th December 1953.

[ClaretTony]

Has to be 48 weeks - first number divisible by both 12 & 16. Therefore codger’s answer of 4th December is correct.

[pushpinpussy]

well done guys. there was me thinking it was difficult

[pushpinpussy]

got another one.

a woman was carrying a basket of eggs. a passerby bumped into her and she dropped the basket and all the eggs broke.

the passerby wanted to pay for the eggs and asked

"how many eggs were in your basket"

i dont remember exactly said the woman but i do recall that whether i divided the eggs by 2,3,4,5 or 6 there was always 1 egg left over.

when i took the eggs out in groups of 7 i emptied the basket.

What is the least number of eggs that broke.

[Bosscat]

Was the port in Spain

[ClaretTony]

If I’ve worked this out correctly it must have been a big basket.

I’ve got an answer if 301.

[pushpinpussy]

well done tony. im giving up. you are too good

[Quickenthetempo]

77 for the 2nd question.

[ClaretTony]

well done tony. im giving up. you are too good

It has to end in an odd number to be one more than divisible by 2 and that left only numbers ending in 1 to be one more than divisible by 5. So I worked from there with numbers divisible by 7.

[bfcmik]

77 for the 2nd question.

76 is not divisible by either 3, 5 or 6

[Quickenthetempo]

76 is not divisible by either 3, 5 or 6

It wasn't supposed to be divisible by any of them. It was divided with one left over.

But it was just a random number guess. 11 is normally a good start with these sort of things so I just times it by 7.

[dsr]

Factorisation. Using factors the lowest number divisible by 2,3,4,5,6 is 60. The number of eggs would be 60+1, but 61 doesn't divide by 7.

So try it with 120 (121 doesn't divide by 7) then 180 then 240 and finally 300, which divides by 2,3,4,5,6 and then add 1 to get 301 which divides by 7.

[Hipper]

If I’ve worked this out correctly it must have been a big basket.

I’ve got an answer if 301.

... or small eggs.

[RalphCoatesComb]

I’ve got an answer if 301.

No wonder she dropped it

[Firthy]

No wonder she dropped it

I wouldn't want to Spot the Ball among that lot

[RalphCoatesComb]

I wouldn't want to Spot the Ball among that lot

You don't want to be around Spot after he's had eggs

[Suratclaret]

301 eggs...that's some omelette. SD must have some player in mind if he's serving that up!

[Bosscat]

301 eggs...that's some omelette. SD must have some player in mind if he's serving that up!

Assuming small eggs at 55g each thats 16 1/2 kilos of eggy mess

[Firthy]

301 eggs...that's some omelette. SD must have some player in mind if he's serving that up!

Maybe he's having BFS round for dinner

[pushpinpussy]

another puzzle. can anyone get it right before CT i ask

3 brothers shared 24 apples each getting a number equal to his age 3 years before. the youngest one proposed a swap

" i will keep only half the apples i got, and divide the rest between you two equally. But then the middle brother, keeping half his accumulated apples must divide the rest between the oldest brother and me, and then the oldest brother must do the same"

They agreed. the result was that each ended up with 8 apples.

How old were the brothers ?

[dsr]

another puzzle. can anyone get it right before CT i ask

3 brothers shared 24 apples each getting a number equal to his age 3 years before. the youngest one proposed a swap

" i will keep only half the apples i got, and divide the rest between you two equally. But then the middle brother, keeping half his accumulated apples must divide the rest between the oldest brother and me, and then the oldest brother must do the same"

They agreed. the result was that each ended up with 8 apples.

How old were the brothers ?

11 year old triplets would work.

In fact I think that's the only thing that would work.

[pushpinpussy]

11 year old triplets would work.

In fact I think that's the only thing that would work.

Sorry DSR thats incorrect

[Im_not_Robbie_Blake]

Mr. Smith is a bank manager.
You have to help him because he has forgotten the combination number of the safe of the bank. Fortunately, he does remember some things about the number which may help you to help him.
•The number has four digits (eg.1234 or 9876).
•All the digits are different.
•It begins and ends with an odd number and has two even numbers in the middle.
•19 and 519 divide it exactly.
What is the number which will open the safe?

[aclaretinstevenage]

9861 - product of 519 x 19 so obviously divisible by both.

[ClaretTony]

11 year old triplets would work.

In fact I think that's the only thing that would work.

Youngest must receive a multiple of 8 apples to ensure he can make his division. It has to be 4 otherwise he wouldn’t be the youngest.

The second receives 1 apple from the youngest and that must take him to a multiple of 4 so he started with 7 which means the oldest had 13 to start.

So ages are 7, 10 & 16.

[dsr]

Sorry DSR thats incorrect

It's the word "accumulated" that fooled me. I might try again in a few hours.

[dsr]

Sorry DSR thats incorrect

7 - 10 - 16

The trick is to start with the youngest one having 4 (because if they aren't triplets, that's the only other multiple of 4 that he can have) and work from there. We know the other two must start with 20 between them because there are 24 in total. There aren't that many options.

[ClaretTony]

7 - 10 - 16

The trick is to start with the youngest one having 4 (because if they aren't triplets, that's the only other multiple of 4 that he can have) and work from there. We know the other two must start with 20 between them because there are 24 in total. There aren't that many options.

See two posts above yours dsr

[dsr]

See two posts above yours dsr

I see it now. Was that an edited version in between when I first read it and when I posted at 5.15? Because I didn't see it then! Of course, it may be old age and senility.

(Mine or yours! )

[pushpinpussy]

i believe CT got it right again.

[Hipper]

Mr. Smith is a bank manager.
You have to help him because he has forgotten the combination number of the safe of the bank. Fortunately, he does remember some things about the number which may help you to help him.
•The number has four digits (eg.1234 or 9876).
•All the digits are different.
•It begins and ends with an odd number and has two even numbers in the middle.
•19 and 519 divide it exactly.
What is the number which will open the safe?

Mr Smith is f.....g idiot!

Why doesn't he just use the year Burnley last won the league, 5960.

Anyway, which bank does he manage?

[Im_not_Robbie_Blake]

claretinstevenage got the bank safe right, having spotted that you only really need the 4th bullet point in order to solve it.

[IanMcL]

well done tony. im giving up. you are too good

The local shop loves him!

There are eggs all over the floor at home and a hell of a big basket!

[Hipper]

Assuming small eggs at 55g each thats 16 1/2 kilos of eggy mess

This is important, isn't it.?

What size basket is required to carry 301 chicken eggs?

From the question we are assuming that we are talking about chicken eggs. A typical chicken egg has a volume of 50ml, or 50cm3. Of course when packing them there will be space between them so let's assume 60cm3 per egg. Times 301 that makes a volume of 18,060cm3.

We are not told anything of the basket size but let's assume that it was one of those weaved shopping basket our Grandmothers would have used. I found one on Amazon:

https://www.amazon.co.uk/Prestige-Wicke ... sic&sr=1-5

It's volume is 28,800cm3, more then adequate for our 301 eggs. Indeed our eggs could occupy 95cm3 each and still be accommodated in the basket.

There's still the question of weight. I assume it must have been Geoff Cape's mother doing the shopping. That would explain how they were carried and why so many eggs were needed.