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.
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)
Math question: In triangle ABC, the angle bisector of angle A intersects BC at point D. If AB = 8 and AC = 10, what is the length of BD?
+
What is the speed(in meters per second) of a car if it travels a distance of 100 meters in 10 seconds?
+
Math Question: Find the absolute extrema of the function f(x) = x^3 - 6x^2 + 9x - 4 on the interval [0, 4].