A farmer is taking her eggs to the market when her cart tips over shattering all of the eggs. She goes to an insurance agent unsure of how many there actually were. She needs to know this to tell the agent though. However, she does know that when she put the eggs in groups of two, there would be one left over. This also seemed to be true for groups of three, four, five, and six. But when she put them in groups of seven, there were an equal number of eggs in each group with none left over.

At first glance, some people might assume the answer is 49 because from simply looking at the problem you would say “Oh, 7 goes evenly into 49, with nothing left over” and from quick thinking you would assume the other numbers would too. But when you try and do the math, you realize that all of the numbers need to go into 48 with 1 left over, and most do, but 5 does not go evenly go into 48 with one left over. So the answer could not possibly be 49.

I began this problem not really sure how to start. I knew that the answer would have to be a multiple of seven so I went from there. Starting from 49 (because I thought it wouldn’t be 49 or lower), I tried each multiple of seven until I got to 140. This is when I started to rethink my strategy, I knew there had to be a more logical way of looking at this. I talked to my friend Michelle who made it clear there was a simpler way of looking at this. She had found the answer by laying out what she knew, and had figured it out from there. So I decided to do the same. I listed everything that I knew about the answer:

The answer had to be a multiple of 7, but 2-6 also had to go into the number before the multiple of 7, so that there would be one left over. So the multiple of seven could not be an even number because it had to have something left over. So I now know that the number is an odd multiple of seven, and I just looked at all of the multiples (not paying attention to the even multiples of 7). I...

...Group 7
Hearts 09-17-10
Period 5
The BrokenEggsPOW #1
1. Problem Statement:
A farmer has some eggs in a cart, and is going to market them. She accidently breaks every egg. She doesn’t remember how many she had, but she remembers some things. She knows that when she put them in groups of 2, 3, 4, 5 and 6, there was one egg left over. When she put them in groups of 13 no eggs were left over. You need to find out how many eggs there are in total.
2. Process:
I first thought about a common multiple of 2, 3, 4, 5, and 6. The least common multiple of those numbers is 60. I know the amount of eggs the farmer has must be a multiple of 60 plus 1. It has to be a multiple of 60 plus 1, because any multiple of 60 plus 1 divided by 2, 3, 4, 5, and 6 will result with a remainder of 1. Then I wrote some multiples of 60 and added 1.
60 | + | 1 | = | 61 |
120 | + | 1 | = | 121 |
180 | + | 1 | = | 181 |
240 | + | 1 | = | 241 |
300 | + | 1 | = | 301 |
360 | + | 1 | = | 361 |
420 | + | 1 | = | 421 |
480 | + | 1 | = | 481 |
540 | + | 1 | = | 541 |
600 | + |...

...Name: Modella Studente POW # 1 BrokenEggs
Problem Statement: How many eggs were broken? (And is there more than one answer?)
Process: Given that she lined them up by twos and one was left over, by threes and one was left over, by fours and one was left over, by fives and one was left over, by sixes and one was left over and by sevens and it came out evenly, we figure the number had to be a multiple of seven and end in a one or a six. (Anything divisible by five with one left over has to end in a one or six: 6, 11, 16, 21, etc. We figure that out when we eliminated 49 as an answer.)
So we started with 21 (the first multiple of seven that ends with a one or a six) and found you couldn't divide by three and have one left over. We went up by sevens until we found 56 (but when we divided by two we didn't have one left over) and 91 (but when we divided by 4 we didn't have one left over) and 136 (which didn't work for two) until we figure out we could go up by 35 to reach the next multiple of seven that ends with a one or a six.
Going up by 35's (161, 206, 231, 276, …) finally led us to 721. An answer that worked! Everyone in the group double-checked it and we found an answer. Now is it the only answer. We realized that the answer had to be odd (because any number divided by two with one left over is odd) so we could go up by 70's.
So we started a new list (791, 861, 931, 1001…) until...

...POW Problem Statement
A. A farmer is going to sell her eggs at the market when along the way she hits a pot hole causing all of her eggs to spill and break. She meets an insurance agent to talk about the incident, and during the conversation he asks, how many eggs did you have? The farmer did not know any exact number, but proceeded to explain to the insurance agent that when she was packing the eggs, she remembered that when she put the eggs in groups of 2-6 she had even groups with 1 left over, but when she put them in groups of 7 she had even groups of 7 with none left over.
B. Why does groups of 2,3,4,5 or 6 results in 1 left over egg, but groups of 7 has an equal amount of eggs with none left over. What # of eggs has equal groups of 2,3,4,5, or 6 with one left over and 7 goes into the number evenly.
C. They think the answer is 49 eggs because 7 goes into 49 eggs evenly with none left over.
D. It cannot be 49 eggs because if it were 49 then 2-6 would need to go into 48 evenly to have a left over egg, but 5 does not go into 48 evenly which is why 49 wouldn’t work
POW Process
A. My initial ideas concerning the task is we need to find a number that has 2,3,4,5 and 6 go into that number evenly with 1 left over and have 7 go into it...

...IMP POW 1: The BrokenEggs
Problem Statement:
A farmer’s cart hits a pothole, causing all her eggs to fall out and break. Luckily, she is unhurt. To cover the cost of the eggs, her insurance agent needs to know how many she had. She can’t remember the number, but can remember some problems she had when packing the eggs. When she put the eggs in groups of two to six eggs, there was always one left over. However, in groups of seven, there were none left over. From what she knows, how can she figure out how many eggs she had?
Process:
First, I thought the answer would be forty-nine. Then, I realized my mistake and tried to think of different ways to do it. I decided to make a chart showing the remainders of the numbers two to six into multiples of seven. I then started to find a pattern. I noticed that the number two has a remainder of one every other multiple of seven, the number three has a remainder of one every two multiples, the number four has a remainder of one every three multiples, and so on. I marked a dot every time there was a remainder of one. I knew that when I had dots marked from two through seven, that would be the answer. So I set out on the long journey of calculating when there was a remainder of one until I reached a number that was all filled up.
Solution:
Using my process, I found that the number of eggs...

...Pow 1
10/6/10
Pow
A farmer is taking her eggs to the market in a cart, but she hits a Pothole, which knocks over all the containers of eggs. When she put the eggs in groups of two, three, four, five, and six there was one egg left over, but when she put them in groups of seven they ended up in complete groups with no eggs left over. Now she needs to know how manyeggs she had and is there more than one possibility.
The first thing I did was to read the pow aging on my own. I out when she put her eggs in groups of two there is one left over. The number cannot be a multiple of two. Also three four five and six can’t be a multiple of this number. If there were no eggs left over when put into groups of seven there must have been a multiple of 7 eggs. Now need to find multiples of seven.
7,14,21,28,35,42,49,56,63,70,77, 84,91,98, 105,112,119,126,133,140,147 ,154,161,168,175,1 82 ,189,196 ,203 ,210, 217, 224, 231 ,238, 245, 252 ,259, 266, 273, 280,287,294,301
Then you cross out all the numbers that are divisible by 2,3,4,5, and 6. So I got161 and 301 as the numbers that cannot be multiples 2, 3,4,5,6.
| 3 * 4 * 7 = 8449 + 84 = 133. No good. 133 is not good because it is not a multiple of 7133 + 84 = 217. No good. 217 because it is not a multiple of 7217 + 84 = 301. Good |...

...The painting Brokeneggs was created by Jean-Baptise Greuze in 1760 and suggests the beginning of the different direction in the art of painting. His work, free of fantasy, introduces new realism – the realism of daily life. French painting during 18th century was dominated by the Rococo style that was aristocratic in nature, sensual and elegant. From stylistic point of view, it had soft colors in its palette, free brushstrokes and complex surfaces. Created for rich patrons, Rococo concentrated on portraits of aristocrats and mythological themes, often performed in a plyful and erotic manner.
Greuze’s moral dramas (one of which is the Brokeneggs) reacted against Rococo. By pronouncing feelings and emotion they were also opposed by the rational and science-oriented representatives of Enlightenment. It puts Greuze’s creations exactly along with other artists in the 18th century who developed the same taste in their works– Taste for Natural.
In this painting by Greuze, the artist depicts a scene from daily life of the middle class with its middle-class morality. The girl has lost her virginity to the young man who was trying to get away, but was stopped by the old lady. The girl’s face is sad and the position of her body suggests the frustration. Her shoulders are weighed down by the heaviness of what happened to her. The brokeneggs next give the narrative quality to the painting and...

...Jean-Baptiste Greuze “BrokenEggs”
By Nina Rettenwander 1756, oil on canvas
The young girl’s body is slumped upon an elevated surface, while her head is tilted to the left at a forty-degree angle. She is draped in a sheer, white blouse and apron, covering a yellow corset and light blue dress. A periwinkle scarf on her head keeps her blonde hair pulled away from her face, revealing her luminescent skin - lit up magnificently by the thin stream of light making its way through the window to her right - and innocent features. The girl’s expression seems to be of pure grief, as she looks down towards the egg basket on the floor; it’s as if she has lost something very dear. This young girl is perhaps saddened at the fact that the egg basket has dropped to the ground and the eggs are now broken. However, the other subject matter in the painting alludes to a larger scale of loss. Immediately above the girl’s left shoulder, a man - appearing about equal in age - stands with his body swaying to his right. His right hip is pointed in the direction of the far left corner of the room, while his head is tilted forty degrees to the right, in the opposite direction of the young girl’s.
One could draw a line straight down the middle of the painting and see that there is symmetry between the young girl’s, and man’s, head. The egg basket is centered in between them, creating a...

...EGGSEggs are laid by females of many different species, including birds, reptiles, amphibians, and fish, and have been eaten by mankind for thousands of years.[1] Bird and reptile eggs consist of a protective eggshell, albumen (egg white), and vitellus (egg yolk), contained within various thin membranes. Popular choices for egg consumption are chicken, duck, quail, roe, and caviar, but theegg most often consumed by humans is the chicken egg, by a wide margin.
Egg yolks and whole eggs store significant amounts of protein and choline,[2][3] and are widely used in cookery. Due to their protein content, the United States Department of Agriculture (USDA) categorizes eggs as Meats within the Food Guide Pyramid.[2] Despite the nutritional value of eggs, there are some potential health issues arising from egg quality, storage, and individual allergies.
Chickens and other egg-laying creatures are widely kept throughout the world, and mass production of chicken eggs is a global industry. In 2009, an estimated 62.1 million metric tons of eggs were produced worldwide from a total laying flock of approximately 6.4 billion hens.[4] There are issues of regional variation in demand and expectation, as well as current debates concerning methods of mass...