The Broken Egg Problem
Day one, getting the problem:
This problem really confused me. I started reading it and it didn't quite make any sense to me. It did, however, make sense to the rest of my group who would obviously have been burdened had I asked, so clarification amongst my group members wasn't exactly something that I was able to pursue. The problem was asking how many eggs a woman had been carrying before she had dropped them. She intended to sell these eggs, so apparently she had insurance on them. The insurance agent had no idea, like me, how many eggs were there, so he asked questions, and the woman was able to recall specific details to aid in the process of finding the egg count. If she organized her eggs in groups of two, there would be a remaining one egg. This trend continued all the way up to six eggs, but when she organized in groups of seven, there was no remainder. So basically, we needed to find a number that when divided by two through six gave a remainder of one. We started two different tactics to complete this problem. One method, which was the more tedious of the two, was to count it out. We started drawing eggs and finding remainders, which wasn't really all the useful. The second method, which was obviously more productive, was the usage of an equation that we decided to try. We tried dividing X by seven in hopes to get the answer of Y, which would hopefully supply the remainder of one. At this point we had run out of time and needed to pack up, so we closed up shop and picked up work the following friday.
Day two, finishing it up:
I really wasn't looking forward to starting this problem today because of how confused I was the previous Friday. Well it turns out that one of my group members felt the same way about me, but he approached it in a different way. Instead of actually trying to solve the problem, he searched it online. You'd be surprised how quickly he managed to find it. He knew the answer and didn't hesitate to tell us, so we used that answer to start finding out exactly how it worked. The answer was 301, so basically we just plugged all the numbers into 301. Since numbers two through six all divided and left a remainder of one, we knew that our numbers couldn't evenly divide. We found this to be true because as expected each number had that one remainder. Then we looked to seven because we knew that it had to be a clean example of division with no remainders. If seven divided evenly into 301, we would know that the bootlegged answer would suffice and give us what we wanted. After a bit of basic division, we found that seven did in fact cleanly divide into 301.
We were on the right track the previous Friday because we were looking at numbers that were divisible by seven that left the remainders. Our first guess was 21, which worked for most numbers, but once we looked at it again we found that it was wrong. This did show, however, that our ideas were on the path to success and that if we hadn't had somebody in the group give us the answer we could very well have answered it on our own.
We were on the right track the previous Friday because we were looking at numbers that were divisible by seven that left the remainders. Our first guess was 21, which worked for most numbers, but once we looked at it again we found that it was wrong. This did show, however, that our ideas were on the path to success and that if we hadn't had somebody in the group give us the answer we could very well have answered it on our own.