## Egg Basket math puzzle

Two children went to town to sell their eggs, one had more in her basket than the other; the one who had the most said to the other, “Give me one of your eggs, and then I shall have double the number you have.”-“No”, said the other; “give me one of yours, and then we shall have equal”.

How many eggs had each of these children?

*(answers to show in 1-2 days) *

Joe| Guest November 12th, 2007 - 11:15 pmx=# of eggs the kid with the most has

y=# of eggs the kid with the least has

x+1=2(y-1)

x+1=2y-2

x=2y-3

x-1=y+1

x=y+2

-(x=2y-3)

0=-y+5

y=5

x=7

guiddeaux| Guest November 12th, 2007 - 11:25 pm1 and 3, i think.^-^

Karen| Guest November 12th, 2007 - 11:41 pm7 and 5. Child with more eggs = x , child with less = y. From the first statement, if 1st gets one more egg, she will have twice what the 2nd has: x + 1 = (y – 1)2 or x = 2y -3 . From the second statement, if 1st gives 2nd 1 egg, they will have an equal number:

x – 1 = y +1 or x = y + 2 . So y + 2 = 2y – 3, then y = 5 and x = 7. I know (mom’s a math geek but I guessed it first, then had to prove it – to myself I guess) Thanks for all the fun – your site is wonderful! (Still no red dot….. yeah!)

Vikram| Guest November 13th, 2007 - 12:56 am7 and 5.

If the girl with more eggs takes one from the other.

7+1=8 which is two times as much as 5-1=4

If the girl with more eggs gives one to the other.

7-1=6 is equal to 5+1=6

Rune| Guest November 13th, 2007 - 3:31 amchild with most egg has 7

child with fewest has 5

7+1= 8 = 2*(5-1)

and

7-1 = 6 = 5+1

Also, I think the children should go for option two

tan| Guest November 13th, 2007 - 4:03 amGirl with most = 5 eggs

Girl with least = 4 eggs

Abhishek| Guest November 13th, 2007 - 5:52 amThe Child with more eggs had 3 eggs and the other had 2 eggs

jason| Guest November 13th, 2007 - 7:34 am7 and 5

Erik| Guest November 13th, 2007 - 8:42 amFirst child (x), Second child (y)

x > y

x + 1 = 2y ; x = y + 1

Answer: First child = 3 eggs, Second child = 2 eggs

Sven| Guest November 13th, 2007 - 9:56 amThe child with more eggs has 7, the child with less has 5.

Let x= number of eggs (more)

Let y = number of eggs(less)

x+1 = 2 (y-1) ; one egg from less to more is twice

x – 1 = y + 1 ; one egg from more to less is equal

Solve for two equations, two unknowns

Mudit| Guest November 13th, 2007 - 10:07 am5 and 7

lily| Guest November 13th, 2007 - 10:11 amthey both have no eggs

Ari| Guest November 13th, 2007 - 10:56 am5 and 7.

MoysieGT| Guest November 13th, 2007 - 11:01 amI think its 7 and 5?

7+1=8, 5-1=4. 8 is double 4 (8 is 2/3rds of the total)

7-1= 6, 5+1=6 Both have equal amounts.

Both numbers are odd. The total number of eggs is even

The total number of eggs can be equaly divisable by 3 without any fractions

etc

Some of my workings are shown bellow

Where it says “Give me one of your eggs, and then I shall have double the number you have.” this indicates this person would then have 2/3rds of the eggs. Also this indicates that this child must have had an odd number of eggs, and now has an even number of eggs. As half of 5 does not go unless half eggs are involved.

For the other side of this where it says “No”, said the other; “give me one of yours, and then we shall have equal”. Indicates the total number of eggs must be an even.

Both children MUST have an odd number of eggs. Child 1 because if given 1 more egg from child 2, would have double that of child 2. Half of an odd number would leave a spare half egg. (Assuming no half eggs are present in this puzzle).

Child 2 because if given 1 more egg from child 1, both would have equal numbers of eggs. sounless half eggs are involved the total number of eggs are even.

The answer could not be 1 and 2 because

1: the total eggs are odd, and

2: subtract 1 from 1 and you would have 0 which you cannot have twice as much as 0.

3: both numbers are not odd

The answer could not be 2 and 4 because

1: Both numbers are even

2: subtract 1 from 2 and add it to 4 gives 5, which is not double 1.

3: 5 is an odd number

etc

The answer could not be 3 and 6 because

1: the total of 3+6 is odd

2: 6 is an even number

3: subtract 1 from3 and add it to 6. 7 is not double 2

4: 7 is an odd number

5: subtract 1 from 6 and add it to 3. 5 is not equal to 4

6: 5 in an odd number

etc

The answer COULD be 5 and 7 becaude

1: both numbers are odd

2: Add 5 and 7 together you get a total of 12 which is even.

3: 12 is equaly divisable by 3 without any fractions.

4: subtract 1 from 5 and add it to 7 which gived you 8 and 4. 8 is double 4

5: 8 is even

6: 8 is 2/3rds of 12

etc

suineg| Guest November 13th, 2007 - 12:00 pmI think one answer can be: child A= 7, child B= 5

explanation:

1) give 1 more and i have the double of yours : A=8, B=4

2)No, give one more and we shall be equal: A=6, B=6

Equations:

from 1) A + 1 = 2(B – 1)

from 2) A – 1 = B + 1

—>B=5—> A=7

Lateral thinking solution i guess(kidding): child A =111, child B=11 give 1 of yours and i shall double the number you have: “1111”, No give one of yours and we should equal: 11-11=0 (definition of equality)

Riyad| Guest November 13th, 2007 - 1:47 pmOne child has x eggs, other has y eggs

1. y gives 1 egg to x

x+1 = 2(y-1) (DOUBLE)

2. x gives 1 egg to y

x-1 = y+1 (EQUAL)

Simplify and we get

y=5, x=7

Q.E.D.

BONNIE| Guest November 13th, 2007 - 2:27 pmone girl had 4 eggs and the other had 5 eggs

Davidmcd| Guest November 13th, 2007 - 3:07 pmanswer is 7 and 5…..girl with 7 takes 1 egg she gets 8 the other girl left with 4 i.e. double, and if the girl with 5 takes 1 egg she gets 6 the other girl left with 6 i.e. equal! easy……..no it was a bit tricky at first!

ian| Guest November 13th, 2007 - 4:11 pm5 and 4 eggs

Mihret K| Guest November 13th, 2007 - 5:14 pmSimple algebra.

x= eggs of person A

y= eggs of person B

1) y+1=2(x-1)

2)y-1=x+1

—Compare them and you get:

x= 5 eggs

y= 7 eggs

That’s it

Shanelly| Guest November 13th, 2007 - 7:32 pmI did trial & error, knowing that the total number of eggs have to be an even number if they can have the equal number of eggs

I got 5 & 7 =12

The mean one who wanted to have double would have had the 7, turned into 8 which would be twice as much as 4

Then, if the mean one actually gave one away, it would be 6 and 6 which would be equal.

nimrod| Guest November 13th, 2007 - 8:04 pmi haven’t thought it through that much, but i think it’s 7 and 5..

rajjo| Guest November 13th, 2007 - 11:19 pm1st child had 7 eggs and 2nd child had 5 eggs

Evie| Guest November 14th, 2007 - 12:02 amOne basket 1 contains 4 eggs & basket 2 has 5 eggs

Jay| Guest November 14th, 2007 - 2:02 am7&5…

Yodhey| Guest November 14th, 2007 - 5:27 amaccording to the question, if the greater no of eggs is say x and lesser no of eggs is say y, then two equations are formed:

x+1 = 2(y-1) and

x-1 = y+1

using these we get,

x = 7 and y = 5

thats it………..

RK| Profile November 14th, 2007 - 9:16 amas we can see from some of the responses submitted above, this one was a bit tricky. Several very good explanations are given for the answer, which is 5 & 7

caleb| Guest November 27th, 2007 - 6:04 pm2 and Zero