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)
Question: "What is the product and sum of a pair of consecutive positive integers from 1 to 10?"
+
What is the radius of a circle if the equation representing its characteristics is x^2 + y^2 = 16?
+
What is the maximum value obtained by the sine function f(x) = sin x?
+
New questions in Mathematics
How much volume of water in MegaLiters (ML) is required to irrigate 30 Hectare crop area with depth of 20mm?
Let 𝑢 = 𝑓(𝑥, 𝑦) = (𝑒^𝑥)𝑠𝑒𝑛(3𝑦). Check if 9((𝜕^2) u / 𝜕(𝑥^2)) +((𝜕^2) 𝑢 / 𝜕(𝑦^2)) = 0
If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.
Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) &lt;2u- 5v,3w&gt;
8x²-30x-10x²+70x=-30x+10x²-20x²
Eight acts are scheduled to perform in a variety show how many different ways are there to schedule their appearances show your work
5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?
A client did not advance L 10,000 for the rental of a parking area and it corresponds to 4 months, of which 2 months were consumed
Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]
what is the annual rate on ​$525 at 0.046​% per day for 3 months?
7/6-(-1/9)
Identify a pattern in the list of numbers.Then use this pattern to find the next number. 37,31,25,19,13
By direct proof, how can you prove that “The sum of any three consecutive even integers is always a multiple of 6”.
I need to know what 20% or £3292.75
The sum of two numbers is 144. Double the first number minus thrice the second number is equal to 63. Determine the first two numbers.
In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24
I. Order to add 40.25+1.31+.45 what is the first action to do ?
1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?
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;
the length of the fenced in area is to be 5 ft greater than the width and the total amount of fencing to be used is 89 ft find the width and length