Tag Archives: Mathematical Morsels

Orange and green dots

Posted on July 8, 2022 by Sumant Sumant
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Why every n-gon has at least n-3 diagonals inside it ?

Posted on July 4, 2022 by Sumant Sumant
Posted in Mathematical Induction, Proof | Tagged , , , | Leave a comment

Where to held the chess tournament ?

Posted on June 30, 2022 by Sumant Sumant
Posted in Graph Theory, Logic | Tagged , | Leave a comment

What ? In complex numbers Fermat’s last theorem doesn’t always hold !!!

Posted on June 30, 2022 by Sumant Sumant
Posted in Algebra, Famous Problem, Number Theory | Tagged , | Leave a comment

Mathematical Morsels by Ross Honsberger

Posted on June 23, 2022 by Sumant Sumant

Problem 1: Chess tournament Problem 1a: Minimizing distance from a fixed point Problem 2: Number of unordered Partitions Problem 3: Regions in a Circle Problem 4: The ferry boats Problem 8: Coloring the plane with 2 colors & rectangle Problem … Continue reading →

Posted in Algebra, Book Notes, Book Review, Number Theory | Tagged , | Leave a comment

Sum of absolute differences of numbers around a circle

Posted on February 13, 2015 by Sumant Sumant

The first positive integers are spotted around a circle in any order you wish and the positive differences between consecutive pairs are determined. Prove that, no matter how the integers might be jumbled up around the circle, the sum of … Continue reading →

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10 point inside a circle, British Olympiad, 1983

Posted on February 13, 2015 by Sumant Sumant

If points are chosen in a circle of diameter , prove that the distance between some pair of them is less than

Posted in Geometry, Pegion Hole | Tagged , , | Leave a comment

A family of equation

Posted on February 8, 2015 by Sumant Sumant

Show that the equation has a rational root between and for all

Posted in Proof, Series | Tagged , | Leave a comment

Counting Triangles

Posted on February 8, 2015 by Sumant Sumant

The rods of lengths can be made to form a triangle if and only if the three triangle inequalities are satisfied: . Suppose one wants to make just one triangle and has at his disposal exactly one rod of each … Continue reading →

Posted in Combinatorics, Geometry | Tagged , | Leave a comment

Quadruple of consecutive integers

Posted on February 8, 2015 by Sumant Sumant

The numbers are divisible by respectively. Can you find consecutive integers divisible by The numbers will be obviously . Now let’s focus on . Now for a difference to be divisible both the numbers should be divisible by . Which … Continue reading →

Posted in Number Theory, Trick | Tagged , | Leave a comment