The next base the essay will explore is base 3 also known as ternary, this is the base that was used in the original Josephus problem. By exploring this base and a few more bases, I will find a pattern and derive an equation to solve Josephus problem with any number of people in any number base.
Josephus problem in base 3 is when each person kills the person who sits two seats away from him and the following diagram will demonstrate how it happens, the numbers on the inside show the order of the people that are gone which will make it easier to follow.
Figure 7 An example of how Josephus problem works in base 3 with 12 people
I will now create the same table as I did for the problem in a binary form.
Table 3 Analyzing the Josephus problem in base 3 when 1≤n≤12
Number of people
()
Order in which people are gone
The winning number
1
1
1
2
1,2
2
3
3,1,2
2
4
3,
…show more content…
Applying the equation to Josephus problem, to find we have to find as . We know how to solve as there are only 2 people and starts meaning he has to skip and therefore dies first and wins. Now we know that , we can see from the table above the answer is correct however we have to do it once more to find .
We can always consider position and we have to repeat the equation until getting to the required number. This solution can be very frustrating as you must do the same thing over and over, however it can be programmed very easily and save a lot of time.
This method is the third and the last method to solve the Josephus problem, it is the most useful method as it works for all bases however it is the most complicated one. In order to compare between this method and the other two methods, we first have to write the equation in base
Joshua is a 25 year old from Westchester Pennsylvania. Out of the three of the young adults
Bales A+C=82, A+D=83, A+E=86, B+C=84, B+D=85, B+E=88, C+D=87, C+E=91, D+E=91. That is just one way to do the problem. My proof that this is the correct answer is because the numbers for each letter added up, equals the weights as given in the book. There are 10 different ways to this problem. I only could figure out one of the ten different ways to do the problem.
The height of the last platform is 12 and the height of the first platform is 4. When we add 4 and 12 the result is 16 and divided by 2 is 8. The 2nd platform is 6 feet and the 4rth platform is 10 feet When added together and divided by 2 to get the average we get 8. The platform is the average number, which is 8. I saw this and put it into a formula. I took the height of the first platform and added it to the last platform, and substituted it for the variables f+l (where l=the height of the last platform). Then I took the total number of platforms and divided it by 2 to get the average, and multiplied it by the average of both platforms to get the total height of all of the platforms. This resulting number is the total length required in square feet of fabric to cover the fronts of the platforms.
Recently, CEO Roger Smith has passed away. Mr. Smith had much success in his lifetime. The CEO stated in his will that he wanted to give his money to his grandchildren. The company board has decided to split his earnings and give it to three of his grandchildren. Each grandchild will receive 5 million dollars. Mr. Smith had always been about helping those in need. The Board chose the three grandchildren that will make a difference with the inheritance. The three grandchildren who were chosen are Fred, Marsha, and Janet Smith.
The participants were three members of a family. The first was male and 67 years of age. The second was female and 52 years old. The third member of the family was male, and 25 years old.
When I came across this question I felt confident in my ability to answer it. Throughout high school I was exposed to many similar questions; because algebra was heavily focused on in my mathematics classes. To answer the question I converted the written instructions into an algebraic statement. So, each sentence was represented by a series of letters and numbers instead of the original words. The algebraic expression that I formed matched one of the possible answers; thus, I felt confident with my final answer.
Literature: Read Remainder of One by Elinor Pinczes to prepare students for the lesson. “What do you think is going to happen in this story? Based on the title, what do you think this has to do with division?” Read the story. “Can anyone tell me how division was used in this book? What happened to the extra 1 person, or the remainder? We are going to learn about dividing larger numbers today and how to do it correctly.”
First, the interviewer presented the problem as difficult when reading the problem. Once the child had solved, the interviewer immediately went to the 7 in the hundreds place and questioned what that number represented (i.e. identifying the place of error). The interviewer pushed the child to re-examine place value, and was able to get the child to realize it should be larger numbers that sum to 1000. However, when the child didn’t automatically try to fix the other numbers, the interview pushed the child to fix the other numbers by again prompting towards place value application. Once the child said ten-hundred, the interviewer pointed back to the previous thousand and questioned why they were different—then asked “Really?” when the child showed a
For this assignment I develop and either pseudo code or a flowchart for my following programming problem.
1, 3, 5, 7, 9, 11, … (The common difference is 2. (Bluman, A. G. 2500, page 221)
Problem Set 2 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 4.
2. When we first began looking at this challenge of finding all the hexominoes, we began by coming up with an assortment that we could think of without using something specific to do so. Then we decided it would be more effective to find all combinations possible by moving one square block. After we were sure we found all of those, we moved on to moving two blocks. We continued doing this by moving three and so forth, until we noticed that we couldn’t move anymore blocks without making the same hexominoes.
This semester I am taking 4 college courses. In all the courses, Math 1325 is the one in which I am facing problems from the beginning of the semester. I am facing difficulty in understanding the lecture of the professor, John Giles, and because of that, I was not able to do my homework all by myself. This is a request from me to please solve this issue as soon as possible.
Teacher Instructions: During large group math, students will act out addition problems at “the bus stop”. Students will take turns being the actors, get a number and sit on the bus with another number. Class will solve the problem of how many the numbers will make before getting off the bus. Next student will write the new number (answer) on the dry erase board.