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
115 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 limit as x approaches 2 of (3x^2 - 8x + 4) / (x - 2)?
+
Math question: Graph the inequality y β‰₯ 2x - 3 on a two-variable graph.
+
Question: How many congruence rules are there in triangle geometry?
+
New questions in Mathematics
calculate the derivative by the limit definition: f(x) = 6x^3 + 2
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
*Question!!* *Victory saved 3,000 in first bank and 2,000 Naira in union bank PSC with interest rate of X% and Y% per annual respectively his total interest in one year is #640. If she has saved 2,000 naira with first bank and 3,000 naira in union bank for same period she would have made extra 20# as additional interest, then find the value of X and Y
Consider numbers from 1 to 2023. We want to delete 3 consecutive, so that the avarage of the left numbers is a whole number. How do we do that
224 Γ— (6Γ·8)
Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A has a bearing of 230Β° and boat B has a bearing of 120Β°. Emma estimates the angles of depression to be about 38Β° for boat A and 35Β° for boat B. How far apart are the boats to the nearest meter?
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. b) What is the profit value made by the hotel for one
Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La TΓͺte CarrΓ©e and is made up of part of a bust that supports a cube divided into five floors. It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3 Calculate, in meters, the height of the bust that supports the cube. Displays all the calculations you made.
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.
Calculate the difference between 407 and 27
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) βˆ’ f(p)| ≀ M|g(x) βˆ’ g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
16.What payment (deposit) made at the end of each month will accumulate to $10473 in 13 years at 7.9% compounded monthly? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
To find the increased amount on a standard term deposit with the following conditions: starting amount: BGN 13000, type of deposit: annual, annual compound interest rate: 1.4%, after 4 years;
Given a circle π‘˜(𝑆; π‘Ÿ = 4 π‘π‘š) and a line |𝐴𝐡| = 2 π‘π‘š. Determine and construct the set of all centers of circles that touch circle π‘˜ and have radius π‘Ÿ = |𝐴𝐡|
2+2020202
Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?
Select a variable and collect at least 50 data values. For example, you may ask the students in the college how many hours they study per week or how old they are, etc. a. Explain what your target population was. b. State how the sample was selected. c. Summarise the data by using a frequency table. d. Calculate all the descriptive measures for the data and describe the data set using the measures. e. Present the data in an appropriate way. f. Write a paragraph summarizing the data.
Recall that with base- ten blocks, 1 long = 10 units, 1flat = 10 long, and a block = 1 unit. Then what number does 5 flat, 17long and 5 units represent represent ?
An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?
Find the number of liters of water needed to reduce 9 liters of lotion. shave containing 50% alcohol to a lotion containing 30% alcohol.

You might be interested in