Yaniv's Gems

Hats in a Line

yaniv — Sun, 16 Nov 2008 00:02:12 +0000

This riddle is a very cool extension of a well known (and easy) riddle, involving people with hats waiting in a line.

So, lets begin with the original:

The Difference Between Area and Volume - Part I

yaniv — Fri, 16 May 2008 13:11:44 +0000

I haven’t written new posts for a while now, as I have been very busy lately.

I think this is a very interesting post and I hope it will make up for the lack of updates. I also want to take this opportunity to thank all of you for posting lots of interesting comments and for sending me many ideas and riddles, thank you!

In this post (and its sequel) I will describe Hilbert’s 3rd problem and show how it is solved. I based the posts mainly on a lecture by Prof. David Gilat.

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Valid Planar Pairing

yaniv — Sat, 24 Nov 2007 16:19:19 +0000

There are 100 red dots and 100 blue dots on the plane (a lot of planar riddles lately). The dots are arranged such that no three are on the same line.

A pairing of the red dots and the blue dots is a one-to-one function that assigns one blue dot to each red dot.

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Uncountable Union

yaniv — Wed, 21 Nov 2007 15:09:42 +0000

A very interesting riddle for those of you with some basic background in Set Theory.

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Expanding Frogs

yaniv — Wed, 21 Nov 2007 14:52:12 +0000

A very easy riddle. Four frogs are sitting on the corners of the unit square (i.e. they have coordinates (0,0), (0,1), (1,1) and (1,0) ). Each turn, a frog can jump over any other frog, thereby transferring itself to the symmetrical point on the other side of the static frog. For example, if the frog at (0,0) jumps over the frog at (1,1) it will land on (2,2).

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Peons

yaniv — Mon, 05 Nov 2007 17:08:45 +0000

This is a cute puzzle. Consider an infinite checkerboard divided in two with an infinite line lying along the x-axis, as depicted below:

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Set it Straight!

yaniv — Wed, 31 Oct 2007 03:08:45 +0000

In this post I will give a basic example of the necessity (or uselessness - its up to you to choose - pun intended) of the axiom of choice. I will also present a less known proof of the Cantor–Bernstein–Schroeder theorem.

The Cantor–Bernstein–Schroeder Theorem

Let A and B be sets. Let f:A->B and g:B->A be injective functions. Then there exists a bijection h:A->B.

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Find the Duplicate

yaniv — Sat, 13 Oct 2007 19:54:35 +0000

Dany Valevsky gave me this very cool riddle.

You are given a vector of size N, the elements of which are numbers in the range 1,…,N-1. I.e. there is at least one repeating element. Give an algorithm that finds a repeating element (it does not matter which one, in case there are several) with O(N) time complexity and O(log(N)) memory complexity.

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Pirates!

yaniv — Sat, 13 Oct 2007 19:45:42 +0000

A ship in the plane has integer coordinates. It also has integer velocity (again in ZxZ). Each turn the ship advances according to its velocity. Here is an example of a ship with velocity (3, 1).

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Turing Machines in Action

yaniv — Sun, 07 Oct 2007 20:49:18 +0000

In this post I will define turing machines and demonstrate a simple one in action.

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