Yaniv's Gems

Rabbit Season

yaniv — Mon, 01 Mar 2010 09:30:56 +0000

There are 10 cells in a line. A transparent rabbit is in one of them. You have a shotgun, and obviously you want to shoot the rabbit.

If you hit the cell with the rabbit, you kill him (and win). Otherwise, if you shoot an empty cell, the rabbit hears the shot, gets scared of the noise and jumps one cell to the right or one cell to the left. In case the rabbit is in the right-most cell, it can only jump to the left (and similarly, if the rabbit is in the left-most cell, it jumps to the right).

Can you kill the rabbit? If so, what is the minimum number of shots needed to guarantee a kill?

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Fat Aunts

yaniv — Wed, 13 Jan 2010 22:16:40 +0000

Two aunts are living each in her own (0-dimensional) house. There are two non-intersecting (1-dimensional) roads between the houses.

Last year, both aunts were doing a lot of exercise, and so they were slim (0-dimensional). They managed to walk together from House 1 to House 2, taking different roads, while each was holding one end of a rope of length less than L.

This year, they gained weight, and each became a sphere of radius L/2. One aunt is in House 1 and the other is in House 2. Can they exchange houses without bumping into each other (their centers must always remain on the roads)?

Really equal? Naturally!

yaniv — Sun, 03 Jan 2010 11:27:15 +0000

You have a set of 2N+1 natural numbers, with the following property: if you remove any one element, you can partition the remaining 2N elements into two sets A and B, each of size N, such that the sum of the N numbers in set A equals the sum of the N numbers in set B. Prove that all the numbers in the original set are equal.

Try to solve the riddle in the more general case, where the numbers are not necessarily natural, but arbitrary reals (some knowledge of algebra is helpful here).

Il Buono, il Brutto, il Cattivo

yaniv — Sun, 05 Jul 2009 20:30:14 +0000

For inspirational music, click here.

Il Buono (nice and easy)

Prove that in a subset of size n+1 of the set {1,2,…,2n} there are two numbers such that one divides the other.

Il Cattivo (beautiful and hard)

Prove that in a sequence of r*s+1 distinct numbers, there is either a monotonically increasing sub-sequence of length r+1 or a monotonically decreasing sub-sequence of length s+1.

Il Brutto (just easy)

Prove that in a subset of size n+1 of the set {1,2,…,2n} there are two relatively prime numbers (i.e. numbers whose gcd is 1).

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Monty Hall Revised

yaniv — Fri, 19 Dec 2008 10:31:44 +0000

This riddle is my take on the Monty Hall problem. If you know the original version, this one should be very easy for you.

You are watching the TV series “Lets Make a Deal”.

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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:

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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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