Category Archives: Problems

Bollobas on solving problems

What you should be terrified of is a blank sheet in front of you after having thought about a problem for a little while. If after a session your wastepaper basket is full of notes of failed attempts, you may … Continue reading

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COMC problem of the week

A nice problem from the 2015 archive filed under week 9, dated 27th October 2015. Define the function [tex]t(n)[/tex] on the nonnegative integers by [tex]t(0)=t(1)=0, t(2)=1,[/tex] and for [tex]n>2[/tex] let [tex]t(n)[/tex] be the smallest positive integer which does not divide … Continue reading

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A Sunday Morning Geometry Problem

It’s 6.15 am on a Sunday morning, 18th October to be exact. The newspapers have not been delivered and the kids are still sleeping. Some peace and quiet for me to do some reading while sipping my morning coffee … … Continue reading

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SEND SOME MORE MONEY

It’s been 9 years since I blogged on SEND MORE MONEY. I got back into this because I found out that the author of SEND MORE MONEY is Henry Dudeney and the puzzle apparently appeared in Strand Magazine vol. 68 … Continue reading

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An identity

The following problem is apparently a bonus question for 13 year olds at a local girls school: Evaluate the sum [tex] \displaystyle \frac{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4} + \cdots + \frac{1}{99} – \frac{1}{100}}{\frac{1}{1+101}+ \frac{1}{2+102} + \cdots + \frac{1}{50+150}}. [/tex] It’s not that easy if … Continue reading

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3.14.15 and Einstein

14 March 2015, was supposed to be the Pi day of the century — for obvious reasons. 14 March is also Einstein’s birthday, and 2015 interestingly marked 100 years of the theory of relativity. I liked this article written by … Continue reading

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Kobon Triangles

Students occasionally have great ideas. Was discussing a problem that originated from some students but was not very well posed. We managed to reformulate it as the maximum number of triangles that can be formed with n lines. This turns … Continue reading

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Prime Mystery

A nice puzzle from Aziz Inan on plus.maths.org The number N represents the first 6 digits of a special number. N consists of three prime numbers put side by side. These three prime numbers come xth, yth and zth on … Continue reading

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The broken stick problem

A slick solution to the broken stick problem or otherwise known as the uncooked spaghetti problem

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That’s an emphatic NO!

all 49% of it. Seen via math-fail.com I was curious about the source and google pointed me here. To restore our sanity, here’s a neat problem from the 2012 AMC 8: Let R be a set of 9 distinct integers. … Continue reading

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Polynomial Puzzle and Lill’s Method

I have in mind a polynomial with nonnegative integer coefficients. Can you determine completely the polynomial by just asking two questions? I forgot where I saw this from but it was interesting enough to spur a few lunch time discussions … Continue reading

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Do you have a problem?

“The man who has no more problems to solve, is out of the game.” – Elbert Hubbard (1856 – 1915), American Writer and Philosopher.

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Can computers write proofs

that human being can understand? By that I mean not those formal logic nonsense. Tim Gowers is doing an interesting experiment to get readers to judge proofs of exercises in metric space theory. The three proofs are supposed to be … Continue reading

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Mathematical Sense Making

I like the following problem. It was shown by Alan Schoenfeld in his talk yesterday in Singapore. Among the many things he touched upon, he introduced the Mathematics Assessment Project which has a package of lessons for grades 6 till … Continue reading

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Social interactions and the development of control strategies

Is a sub section in Schoenfeld’s Mathematical Problem Solving. The argument is that when two students work together, this interaction can spur cognitive development resulting in approaches to the problem being solved that are qualitatively different than those taken by … Continue reading

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Geometry Puzzle

A neat little puzzle from John Mason. How are the blue and red area related?

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What is real world mathematics?

According to Tim Gowers, real world mathematics is not really about disguising equations into apples and pears.

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The Feynman Problem Solving Algorithm

according to here is this 1) Write down the problem 2) Think very hard 3) Write down the answer

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Nice geometry problem

From the MAA minute math! a problem on 3d geometry. I must confess I peeped at the hint.

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The time to work on a problem

the time to work on a problem is after you’ve solved it — R. H. Bing Extracted from the book “The 5 elements of effective thinking.” Put the exact quote in google books to locate it. Seen via jd cook.

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