$MathMaster logo$

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)

How many students prefer math over science in a class of 30? (Give your answer as a whole number)

+

What is the slope of the linear function f(x) = x?

+

What is the value of constant c if the function f(x) = c is represented by a straight horizontal line on the coordinate plane?

+

New questions in Mathematics

Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps

If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.

The Lenovo company manufactures laptop computers, it is known that for every 60 laptops produced, 54 go on the market with the highest quality standards. If a sample of 15 laptops is taken, calculate the probability that: Exactly 2 are not of high quality

A soft drink machine outputs a mean of 23 ounces per cup. The machines output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 26 and 28 ounces round your answer to four decimal places

(2x+5)^3+(x-3)(x+3)

"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?" The answer is the number of response units.

The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?

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?

You are the newly appointed transport manager for Super Trucking (Pty) Ltd, which operates as a logistics service provider for various industries throughout southern Africa. One of these vehicles is a 4x2 Rigid Truck and drawbar trailer that covers 48,000 km per year. Use the assumptions below to answer the following questions (show all calculations): Overheads R 176,200 Cost of capital (% of purchase price per annum) 11.25% Annual License Fees—Truck R 16,100 Driver Monthly cost R 18,700 Assistant Monthly cost R 10,500 Purchase price: - Truck R 1,130,000 Depreciation: straight line method Truck residual value 25% Truck economic life (years) 5 Purchase price: Trailer R 370,000 Tyre usage and cost (c/km) 127 Trailer residual value 0% Trailer economic life (years) 10 Annual License Fees—Trailer R 7,700 Fuel consumption (liters/100km) 22 Fuel price (c/liter) 2053 Insurance (% of cost price) 7.5% Maintenance cost (c/km) 105 Distance travelled per year (km) 48000 Truck (tyres) 6 Trailer (tyres) 8 New tyre price (each) R 13,400 Lubricants (% of fuel cost) 2.5% Working weeks 50 Working days 5 days / week Profit margin 25% VAT 15% Q1. Calculate the annual total vehicle costs (TVC)

The maximum gauge pressure of a hydraulic ramp is 16 atm, with a support area whose diameter is 20 cm. What is the mass of the heaviest vehicle that can be lifted?

A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 60% of the people get vaccinated. If a person is selected at random from this region, find the probability that he or she will contract the disease. (4 Points)

Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0

Two minus log 3X equals log (X over 12)

How do you convert a fraction to a decimal

The average weekly earnings in the leisure and hospitality industry group for a re‐ cent year was $273. A random sample of 40 workers showed weekly average ear‐ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% con‐ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.

-6 - t / 4 = -1

Emile organizes a community dance to raise funds. In addition to paying $300 to rent the room, she must rent chairs at $2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for $7 each. How much should she sell to raise money?