## Postage stamp denominations

Posted on: April 30th, 2013 by
A set of k positive integers is a postage stamp basis for n if every positive integer up to n can be expressed as the sum of no more than h values from the set. An extremal basis is one for which n is as large as possible. Design an extremal postage stamp basis (maximize n) with k=8 denominations such that every integer <= n Continue reading the story "Postage stamp denominations"

## A logic puzzle

Posted on: April 29th, 2013 by
Albert is looking at Betty. Betty is looking at Charlie. Albert is a computer programmer. Charlie is not. Is there a computer programmer looking at a non-computer programmer? Answer should be “Yes”, “No” or “Not Enough Information”. Hint: Don't rush, think for a while. via Math Factor

## Guessing Polynomials

Posted on: April 28th, 2013 by
Player 1 thinks of a polynomial P with coefficients that are natural numbers. Player 2 has to guess this polynomial by asking only evaluations at natural numbers (so one can not ask for P(π)). How many questions does the second player need to ask to determine P? via Math Overflow Solution can be found here Hint: ... ... ... ... ... ... ... ... ... ... ... ... You can find the polynomial in 2 attempts.

## Rolling coins

Posted on: April 27th, 2013 by
There are 2 puzzles today. The easier puzzle first: Roll a penny around another fixed penny in the center with edges in close contact. After moving half circle around the center penny, you will find the penny in motion has rotated 360 degrees. Why? via CSE blog Now for the harder puzzle: Place four \$1 coins as shown in the diagram below: Now roll the shaded coin Continue reading the story "Rolling coins"

## Nim game

Posted on: April 26th, 2013 by
The game of Nim is played between 2 players A and B: There are 3 heaps numbered 1,2,3. Each heap contains 10 rings. Players take turns removing rings from heaps. In each turn, a player chooses a heap and removes as many rings as he wants from the heap. He cannot remove rings from more than one heap in a single turn. This continues until Continue reading the story "Nim game"

Posted on: April 25th, 2013 by
Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle? Obviously the probability depends on how you choose the random chord. Suppose you require the following additional constraints for choosing how the chords must be chosen: Assume that chords are laid at random onto Continue reading the story "Bertrand's paradox"

## Toy Fermat

Posted on: April 24th, 2013 by
3

Does the equation, x^2 + y^3 = z^4 have solutions in prime numbers? Find at least one if yes, give a nonexistence proof otherwise. via Math puzzles

## Candy game

Posted on: April 23rd, 2013 by
4

A group of students are sitting in a circle with the teacher in the center. They all have an even number of candies (not necessarily equal). When the teacher blows a whistle, each student passes half his candies to the student on his left. Then the students who have an odd number of candies obtain an extra candy from the teacher. Show that after a Continue reading the story "Candy game"

## Black and white squares

Posted on: April 22nd, 2013 by