Tag Archives: NPTEL

NPTEL Number theory 9^9^9 mod 100 is 89

Posted on August 14, 2023 by Sumant Sumant

if then is ?

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NPTEL Number theory 5^5^5 mod 50 is 25

Posted on August 14, 2023 by Sumant Sumant

if then is ?

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Why edge coloring of K17 graph with three colors will have a monochromatic triangle ?

Posted on July 27, 2023 by Sumant Sumant
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A fun problem on connectivity of Graph from NPTEL exam

Posted on March 26, 2023 by Sumant Sumant

Given a graph on 20 vertices . Is the graph connected?

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Number of surjective functions

Posted on October 13, 2022 by Sumant Sumant

Number of surjective functions is given by when there are n number if elements in the domain and k number of elements in the range. Note this is same as labeled balls in labeled bucket with the condition no bucket … Continue reading →

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Why any 10 random 4 element subsets made out of 11 elements always have at least 2 sets with 2 or more common elements ?

Posted on July 26, 2022 by Sumant Sumant

Let S be an 11 element set. Consider any 10 four element subsets of S. Thentwo of these must share greater than or equal to 2 common elements.

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Why there always exists a mid point with integer coordinates among 9 random points with integer coordinates ?

Posted on July 25, 2022 by Sumant Sumant

Consider 9 points with integer coordinates in . Show that midpoint of the line joining some pair of points also has integer coordinates.

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Combinatorics Assignment 0

Posted on July 13, 2022 by Sumant Sumant
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Minimum Spanning Tree and inclusion of edges with max and min weight

Posted on February 14, 2022 by Sumant Sumant

Let G=(V,E) be an undirected and connected graph having more that $late |V|-1 $ edges. G has a unique heaviest edge , then cannot be part of a minimum spanning tree ?

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Average degree and number of vertices in a tree

Posted on February 14, 2022 by Sumant Sumant

Let T be a tree with average degree L. Then the number of vertices in T equals ?

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