Question
In: Advanced Math
A number of guests gather around a round table for a dinner. Between every adjacent pair...
A number of guests gather around a round table for a dinner. Between every adjacent pair of guests, there is a plate for tips. When everyone has finished eating, each person places half their tip in the plate to their left and half in the plate to their right. Suppose you can only see the amount of tips in each plate after everyone has left. Can you deduce the amount that each individual tipped?
(a) Suppose six guests sit around a table and there are six plates of tips. If we know the amount of tip in each plate, P1 to P6, can we determine each individual’s tip amount, G1 to G6 (G1+G6 = P1, G1+G2 = P2, G2+G3 = P3, ... , G5+G6 = P6)? If yes, explain why by examining the relationship between the plate values, P1 to P6, and guest tips, G1 to G6. If not, give two different assignments of G1 to G6 that will result in the same P1 to P6.
(b) Now lets consider five guests at the table, G1 to G5, and we can see the amount of tips in the five plates, P1 to P5 ((G1+G5 = P1, G1+G2 = P2, G2+G3 = P3, ... , G4+G5 = P5)). In this new setting can you figure out each guests tip values, G1 to G5?
(c) If n is the total number of guests sitting around a table, for which values of n can you figure out everyone’s tip? You do not have to rigorously prove your answer. (Hint: consider what is different about parts a and b.)
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Let T be a graph. Suppose there is a unique path between every pair of vertices...
Let T be a graph. Suppose there is a unique path between every
pair of vertices in T. Prove that T is a tree.
Can I do this using the contraposative? Like Let u,v be in T and
since I am assuming T to not be a tree this allows cycles to occur
thus the paths must not be unique. Am I on the right track?
Using C language Problem description n (n is odd) people sitting around a round table playing...
Using C language
Problem description
n (n is odd) people
sitting around a round table playing a game. In this situation,
everyone has a left neighbour and a right neighbour. At the
beginning, each of them is holding a whiteboard with an integer
number. Now, they are playing a game consisting of several rounds.
In each round, everyone will first look at the numbers of his/her
left neighbour and right neighbour, then calculate the average of
the two numbers, replace...
Use the method of exhaustion to prove the following statement: “For every prime number p between...
Use the method of exhaustion to prove the following statement:
“For every prime number p between 30 and 58, 10 does not divide p −
9.”
Prove that 0.17461461 . . . is rational (digits 461 in the
fractional part are periodically repeated forever).
The following data in the table below represents the relationship between the number of workers and...
The following data in the table below represents the
relationship between the number of workers and their outputs in a
company for a given day in the short-run:
Workers
Output
P
Marginal Product
MP
Variable Cost
VC
Fixed Cost
FC
Total Cost
TC
Average Variable Cost
AVC
Average Fixed Cost
AFC
Average Total Cost
TC
Marginal Cost
MC
0
0
0
1
12
2
2
21
6
3
27
12
4
30
35
5
32
80
6
33
160
1- ...
The following data in the table below represents the relationship between the number of workers and...
The following data in the table below represents the
relationship between the number of workers and their outputs in a
company for a given day in the short-run:
Workers
Output
P
Marginal Product
MP
Variable Cost
VC
Fixed Cost
FC
Total Cost
TC
Average Variable Cost
AVC
Average Fixed Cost
AFC
Average Total Cost
TC
Marginal Cost
MC
0
0
0
1
12
2
2
21
6
3
27
12
4
30
35
5
32
80
6
33
160
Q1...
10. Write a for loop which will print every number evenly divisible by 13 between 1...
10. Write a for loop which will print every number evenly
divisible by 13 between 1 and 100, inclusive. Your loop will only
increment by 1 each loop so you need an if test to see if each
number should be printed. Put each number output on the
same line, 1 space apart.
11. Write a while loop which will prompt the
user for a number and accept their input and then display this
message (assuming number input is 3)...
The following table shows the daily relationship between the number of workers and output (Q) for...
The following table shows the daily relationship between the
number of workers and output (Q) for a small factory in the short
run, with capital held constant. Each worker costs $200 per day,
and the firm has fixed costs of $100 per day. Calculate total
cost (TC), marginal cost (MC), and average total cost
(ATC). (Round your answers to two decimal places.)
WORKERS Q TC MC ATC
1 20 ? ? ?
2 44 ? ? ?
3 70...
Refer to the table below. Consider the relationship between the number of houses sold (Y) and...
Refer to the table below. Consider the relationship between the
number of houses sold (Y) and the mortgage rate (X). The values of
X and Y for twelve (12) months are shown in the table below.
M-Rates 8 9.5 7.5 11 8.5 10 10.5 7 7.5 11 9 8 Houses sold 188 145
181 137 157 148 140 203 188 144 150 166 Based on that, a. Calculate
the coefficient of correlation between the number of houses sold
and the...
The table below shows the weekly relationship between output and number of workers for a factory...
The table below shows the weekly relationship between output and
number of workers for a factory with a fixed size of plant.Number
of Workers Output001502110330044505590666577008725971010705a.
Calculate the marginal product of labor. b. At what point do
diminishing returns set in? Explain. c. Based on the table above,
if the wage rate is $500.00 and the price of output is $5, how many
workers should the firm hire?
in JAVA, Hash table The goal is to count the number of common elements between two...
in JAVA, Hash table
The goal is to count the number of common elements between two
sets. Download the following data sets, and add them to your
project:
girlNames2016.txt
boyNames2016.txt
These files contain lists of the 1,000 most popular boy and girl
names in the US for 2016, as compiled by the Social Security
Administration. Each line of the file consists of a first name, and
the number of registered births that year using that name.
Your task is to...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Consider a buffer system consisting of Benzoic acid (pKa = 4.20) and sodium benzoate, a) Would...
- Decision Variables S T Minimize 1.8S + 2.20T Subject to: Potassium 5S + 8T >= 200...
- A neurologist needs to counsel a stroke victim and her husband about possible outcomes, treatment options,...
- Case Study: Personal Beliefs in the Workplace Don Shakow was a prominent professional who worked in...
- 1: Competency framework usage is the modern best practice in management. What is meant by competency...
- A 19.34 g mixture of sugar (C12H22O11) and table salt (NaCl) is dissolved in 231 g...
- Young and Company claims that its pressurized diving bell will, on average, maintain its integrity to...
ADVERTISEMENT