Math Is Fun Forum

anandbrar

Member

Registered: 2011-07-20

Posts: 70

The Egg-seller's eggs..

An egg-seller was on his way to a village. On his way, a fool collided with him and all his eggs broke. They both went to the village head-man. When the head-man asked how many eggs he had, the egg-seller told him,

"When counted in twos, 1 remains,
When counted in threes, 2 remain,
When counted in fours, 3 remain,
When counted in fives, 4 remain,
When counted in sixes, 5 remain,
When counted in sevens, none remain...
I had less than 150 eggs."

How many eggs did he have?

Last edited by anandbrar (2011-07-21 06:39:49)

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"widen your gaze... extend beyond the obvious..."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: The Egg-seller's eggs..

hi anandbrar

I got

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: The Egg-seller's eggs..

hi anandbar

yup i did this problem except it wasn't bout eggs.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
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anandbrar

Member

Registered: 2011-07-20

Posts: 70

Re: The Egg-seller's eggs..

hi bob bundy, anonimnystefy

Both your ans are correct.

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"widen your gaze... extend beyond the obvious..."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Egg-seller's eggs..

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anandbrar

Member

Registered: 2011-07-20

Posts: 70

Re: The Egg-seller's eggs..

hi bobbym,

why did you multiply with 3*3*...?

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"widen your gaze... extend beyond the obvious..."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Egg-seller's eggs..

Hi;

Each mutiplication does not effect the solution set. But you multiply until the number is congruent to 1 for the modulo. This has the effect of solving for the variable.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anandbrar

Member

Registered: 2011-07-20

Posts: 70

Re: The Egg-seller's eggs..

Hi, I had a query..

If he were to say:

"When counted in twos, 1 remains,
When counted in threes, 2 remain,
When counted in fours, 3 remain,
When counted in fives, 4 remain,
When counted in sixes, 5 remain,
When counted in sevens, 6 remain,...
so on till
When counted in elevens, none remain"

Will the least answer be 30239?

Could anyone verify if this would be the least answer...thanks..

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"widen your gaze... extend beyond the obvious..."

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,421

Re: The Egg-seller's eggs..

Hi anandbrar,

I think the answer would be 2519.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Egg-seller's eggs..

Hi;

2519 that is what I am getting also.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

sandesh234

Member

Registered: 2011-08-17

Posts: 7

Re: The Egg-seller's eggs..

My answer

Muramal

Member

Registered: 2011-12-17

Posts: 1

Re: The Egg-seller's eggs..

Got it
The question clearly says less than 150 eggs
So why do we have answers by the xxxxxdigits?

It's simply 119 eggs!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Egg-seller's eggs..

Hi Muramal;

Welcome to the forum. This should clear up the confusion.

Everyone did answer 119 ( see post #2,3 and 5).

The higher number (2519) was for the second problem (post #8) which does not have the <120 restriction.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: The Egg-seller's eggs..

Suppose we are looking for x, where x is the number of eggs. Then x+1 should be a multiple of 2,3,4,5,6.
The smaller number to meet this criteria is 5x12 = 60, then 120, then 180 etc.
Moreover, x should be a multiple of 7, thus (x+1)mod7 = 1, thus 120-1 = 119, 238 etc.
The number also has to be <150, so it is 119.