# Category Archives: Problems

## 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

## 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

## 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

## Geometry Puzzle

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

## What is real world mathematics?

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

## The Feynman Problem Solving Algorithm

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

## Nice geometry problem

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

## 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.

## 16 Plates

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

## An AMC problem on sieveing primes

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

## A dicey past year exam question

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

Let $a_n$ 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