Category Archives: Problems

Can computers write proofs

Posted on 8/4/2013 by tpc

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 →

Posted in Geometry/Topology, Problems, Technology | Leave a comment

Mathematical Sense Making

Posted on 8/2/2013 by tpc

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

Posted on 14/12/2012 by tpc

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

Posted on 5/12/2012 by tpc

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

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What is real world mathematics?

Posted on 4/11/2012 by tpc

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

Posted in Applications, Learning, Problems, Teaching | Leave a comment

The Feynman Problem Solving Algorithm

Posted on 21/10/2012 by tpc

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

Posted on 27/9/2012 by tpc

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

Posted on 27/8/2012 by tpc

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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16 Plates

Posted on 9/8/2012 by tpc

An interesting problem from the wordplay column of the New York Times. Can you arrange plates numbered 1 to 16, in a circle so the sum of adjacent pairs is always a perfect square? The quick answer is no, since … Continue reading →

Posted in Number Theory, Problems | Leave a comment

An AMC problem on sieveing primes

Posted on 30/6/2011 by tpc

The following is an AMC 12 problem from 2005, courtesy of the MAA Minute Math. Follow the link for an interactive version complete with hints, solutions and difficulty hosted on MAA.org. Problem: Call a number “prime-looking” if it is composite … Continue reading →

Posted in Combinatorics, Number Theory, Problems | Leave a comment

A dicey past year exam question

Posted on 13/5/2011 by tpc

A die consists of six faces with each face representing precisely one of the numbers 1, 2, 3, 4, 5, 6. Suppose that n such dice are rolled for some positive integer n. The number of the upper face of … Continue reading →

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Modelling with exponential generating functions

Posted on 13/5/2011 by tpc

Let [tex] a_n[/tex] be the number of ways to distribute n distinct objects to four distinct boxes, such that the total objects is even. Find the exponential generating function. Either all four boxes have even number of objects, or exactly … Continue reading →

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A nonlinear first order recurrence relation

Posted on 13/5/2011 by tpc

Mr Ding! asked me the following question from Bona’s textbook. Question 6 of supplementary exercises in chapter 3. [tex] a_n = (n+1) a_{n-1} +3^n, a_0 = 1[/tex] My solution as follows. Let [tex]b_{n+1} = a_n [/tex]then [tex] b_{n+1} = (n+1) … Continue reading →

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12 Days of Christmas

Posted on 21/12/2010 by tpc

Nice problem and solution at squarecirclez about counting the total number of presents. Triangular numbers appears! It seems that this year’s Simpsons Christmas special was a live action parody/tribute to Sesame Street and the Muppets. It had them singing the … Continue reading →

Posted in Calculus/Analysis, Fun Stuff, Number Theory, Problems, Teaching, Technology | Leave a comment

To the fourth dimension …

Posted on 1/4/2010 by tpc

and beyond? xkcd mentioned this game Miegakure about puzzle solving in four dimensions. I have my doubts about this but it’ll certainly be interesting.

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Another neat number puzzle

Posted on 8/4/2009 by tpc

I chanced upon this neat number puzzle devised by William Wallace, via wild about maths. It’s form is certainly recognizable, but still the effort deserves praise. I remember a similar puzzle played with a deck of cards. You lay out … Continue reading →

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Separating the variables

Posted on 13/1/2009 by tpc

We should all be familiar with the method of separation of variables for first order ordinary differential equations. Here’s a neat example from John Starrett’s article in Amer. Math. Monthly. [tex] \displaystyle \frac{dy}{dx} = \frac{ y^3 + x^2y -x -y}{ … Continue reading →

Posted in Calculus/Analysis, Problems | Leave a comment

Einstein’s Puzzle

Posted on 6/5/2008 by tpc

I’ve been looking at logic puzzles as a break from all the frenzied examination related activities. An internet search will inevitably throw up the old nugget known as Einstein’s IQ quiz or puzzle. The wiki entry has a variant called … Continue reading →

Posted in Fun Stuff, Problems | 1 Comment

Solving Mathematical Problems

Posted on 19/6/2007 by tpc

a personal perspective by Terence Tao. This is a new edition of a book which was written by Tao more than 15 years ago, which means when he was only 15! It’s a thin little book that takes a leisurely … Continue reading →

Posted in Books, Problems | 1 Comment

Trigonometric problem

Posted on 30/4/2007 by tpc

Here’s my solution to a nice little trigonometric problem posted by miss loi. Show that [tex]\frac{ \tan x + \sec x – 1} { \tan x – \sec x +1 } \equiv \tan x + \sec x[/tex] [tex]\frac{ \tan x … Continue reading →

Posted in Problems | 3 Comments