Tag Archives: Polya

Slicing hexagon into two equal parts

Posted on August 4, 2022 by Sumant Sumant

Given a regular hexagon and a point in its plane. Draw a straight linethrough the given point that divides the given hexagon into two partsof equal area.

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Bob and his 10 pockets

Posted on August 4, 2022 by Sumant Sumant

Bob has 10 pockets and 44 silver dollars. He wants to put his dollars intohis pockets so distributed that each pocket contains a different number ofdollors. Can he do so ?

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Conjecturing and proving the sum of the series

Posted on August 4, 2022 by Sumant Sumant
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Find sides of a right angled triangle given its perimeter and altitude length incident on hypotenuse

Posted on August 3, 2022 by Sumant Sumant

Find sides of a right angled triangle whose perimeter is 60 and length of altitude incident on hypotenuse is 12

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Number of digits used for page numbering

Posted on August 3, 2022 by Sumant Sumant
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A quartic equation with roots in arithmetic progression

Posted on August 3, 2022 by Sumant Sumant
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Using 4 and 9 quart pails to measure 6 quarts

Posted on August 1, 2022 by Sumant Sumant

How can you bring up from the river exactly six quarts of water when you have only two containers, a four quart pail and a nine quart pail ?

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How to draw an inscribed square in any triangle ?

Posted on July 23, 2022 by Sumant Sumant

https://www.geogebra.org/classic/atnzjncs

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Another way to prove why it is not possible to use each digit from 0 to 9 to come up with a sum of 100.

Posted on July 21, 2022 by Sumant Sumant

The insight for this proof came from a fellow math teacher Abraham Gurrero Julio who responded to my earlier writeup on Linkedin. Thank Abraham Gurrrero.

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Why its not possible to use each digit from 0 to 9 only once to come up with an exact sum of 100 ?

Posted on July 20, 2022 by Sumant Sumant
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