MathMaster logo

MathMaster

  1. Home
  2. general
  3. prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that t
Question

Prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that the sum of the numbers in each of the columns is the same.

176

likes
879 views

Answer to a math question Prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that the sum of the numbers in each of the columns is the same.

Expert avatar
Miles
4.9
114 Answers
sum of natural numbers from 1 to 240 =\frac{240\times241}{2}=28920 number of columns = 16 for equality, each slumn should have the sum as 28920/16 = 1807.5 which is a fractional number we are only putting integers, and hence sum of each column has to be an integer and Not a fraction. Hence the given statement is proved

Frequently asked questions (FAQs)
What is the variance of the following data set: 5, 8, 12, 15, 18?
+
What is the derivative of y = cos(2x) at x = π/3?
+
What is the period of the trigonometric function f(x) = 3 cos(4x) + 2sin(2x)?
+
New questions in Mathematics
A particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:40 a.m. Round your answer to four decimal places, if necessary.
-x+3x-2,si x=3
To calculate the probability that a player will receive the special card at least 2 times in 8 games, you can use the binomial distribution. The probability of receiving the special card in a single game is 1/4 (or 25%), and the probability of not receiving it is 3/4 (or 75%).
11(4x-9)= -319
A car tire can rotate at a frequency of 3000 revolutions per minute. Given that a typical tire radius is 0.5 m, what is the centripetal acceleration of the tire?
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
What is the amount of interest of 75,000 at 3.45% per year, at the end of 12 years and 6 months?
A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had
The mean temperature for july in H-town 73 degrees fahrenheit. Assuming that the distribution of temperature is normal what would the standart deviation have to be if 5% of the days in july have a temperature of at least 87 degrees?
Divide 22 by 5 solve it by array and an area model
Suppose you have a sample of 100 values from a population with mean mu = 500 and standard deviation sigma = 80. Given that P(z < −1.25) = 0.10565 and P(z < 1.25) = 0.89435, the probability that the sample mean is in the interval (490, 510) is: A)78.87% B)89.44% C)10.57% D)68.27%
Determine the increase of the function y=4x−5 when the argument changes from x1=2 to x2=3
The probability of growing a seedling from a seed is 0.62. How many seeds do I need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87?
Sections of steel tube having an inside diameter of 9 inches, are filled with concrete to support the main floor girder in a building. If these posts are 12 feet long and there are 18 of them, how many cubic yards of concrete are required for the job?
Let x be an integer. Prove that x^2 is even if and only if is divisible by 4.
solid obtained by rotation around the axis x = -1, the region delimited by x^2 - x + y = 0 and the abscissa axis
You buy a $475,000 house and put 15% down. If you take a 20 year amortization and the rate is 2.34%, what would the monthly payment be?
2+2020202
Write decimal as the fraction 81/125 simplified
(3.1x10^3g^2)/(4.56x10^2g)

You might be interested in