$MathMaster logo$

MathMaster

Home
general
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.

$Expert avatar$

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 value of sinh(cos^-1(1/3))?

+

What is the equation of an ellipse with center (3,-2), major axis length 10, and minor axis length 6?

+

Math question: What is the smallest positive integer solution to x^n + y^n = z^n, where n>2 according to Fermat’s Theorem? (

+

New questions in Mathematics

Karina has a plot of 5,000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used for cultivation?

Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)

2x-4y=-6; -4y+4y=-8

Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?

We have spent 1/4 of the inheritance on taxes and 3/5 of the rest on buying a house. If the inheritance was a total of €150,000 How much money do we have left?

A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?

How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.

4x + 8y = 5 2x + 4y = 10

How many square feet of floor area are there in three two-storey apartment houses, each of which is 38 feet wide and 76 feet long?

The sick-leave time of employees in a firm in a month is normally with a mean of 100 hours and a standard deviation of 20 hours. Find the probability that the sick-leave time of an employee in a month exceeds 130 hours.

A tree cast a shadow of 26 meters when the angle of evaluation of the sum is 24°. Find the height of the tree to the nearest meter

In a physics degree course, there is an average dropout of 17 students in the first semester. What is the probability that the number of dropouts in the first semester in a randomly selected year has between 13 and 16 students?

A multiple choice exam is made up of 10 questions; Each question has 5 options and only one of them is correct. If a person answers at random, what is the probability of answering only 3 good questions?

7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?

Identify the slope and y intercept y=11+2/3x

A nondegenerate ideal gas of diatomic molecules with a kilomolar mass of 2 kg/kmol and a characteristic rotational temperature of 86 K is adsorbed on the walls of a container, where the binding energy is 0.02 eV. The adsorbed molecules move freely on the walls, and their rotation is confined to the plane of the walls. Calculate the surface density of adsorbed molecules at 12 K if the gas pressure is 103 Pa! What result would you get at 68 K and the same pressure?

A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.

Let A denote the set of all people who were alive in 2010. Let B denote the set of all real numbers. Let f assign, to each person in A, their weight during the year 2010. Is f a function? Explain in complete sentences.