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: "Graph the inequality y ≤ 2x + 5 on a coordinate plane."
+
Math question: If a triangle has side lengths of 6, 8, and 10 units, what is its area using Heron's Formula?
+
What is the length of the hypotenuse of a right triangle with legs measuring 3 and 4 units?