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**anandbrar****Member**- Registered: 2011-07-20
- Posts: 70

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)*

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,374

hi anandbrar

I got

Bob

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: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

hi anandbar

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

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

hi bob bundy, anonimnystefy

Both your ans are correct.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anandbrar****Member**- Registered: 2011-07-20
- Posts: 70

hi bobbym,

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anandbrar****Member**- Registered: 2011-07-20
- Posts: 70

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..

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,351

Hi anandbrar,

I think the answer would be 2519.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Hi;

2519 that is what I am getting also.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**sandesh234****Member**- Registered: 2011-08-17
- Posts: 7

My answer

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**Muramal****Member**- Registered: 2011-12-17
- Posts: 1

Got it

The question clearly says less than 150 eggs

So why do we have answers by the xxxxxdigits?

It's simply 119 eggs!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anna_gg****Member**- Registered: 2012-01-10
- Posts: 113

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.

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