Puzzle #141: Wolfs and Sheep

This is a “addictive” problem – hard to get rid of until you solve it. Thanks to Pooja Goyal, my wife, who gave me this puzzle a few days back from a  Math festival she was at.

Place 5 wolves and 3 sheep in the grid in such a way that no wolf can get to (and eat) any of the sheep. A wolf can move in a straight line any number of squares up or down, left or right, or diagonally.
Note: You must have exactly 5 Wolves and 3 Sheep on the grid.

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy Sunday!

Posted in Puzzles | Tagged , | 4 Comments

Solution to Puzzle #139: Gold Links

Apologies for skipping last weekend, I was traveling on work!

I got correct answers from three people – Pratik Poddar, Abhinav Jain and Suman Saraf. Well done!

Most people thought binary, i.e. have links of size 1, 2, 4, 8, ….while that will work, we need to recognise that the link opens on both side, and once opened, you gave a chain of the size of “1” from the opened link. Therefore for each opened link, you will have a chain of “1”. The optimal will be to cut the fourth and the eleventh link which will create the following parts:

1,1,3,6,12

This would mean 2 cuts are enough xxx|xxxxxx|xxxxxxxxxxxx (where | are the links we open)

Hope you all enjoyed the puzzle!

 

Posted in Solution | Tagged , | Leave a comment

Puzzle #140: Traffic Flow in Floyd’s Knob – Version 2

As I mentioned in the answer for Puzzle #138, I ended up posting the original version of the puzzle and not the one posted by Martin Gardner. I like the puzzle so much, that I am posting the variation from Martin Gardner here. Repeating the puzzle here.

TrafficFlowInFloydsKnob

“Because the town of Floyd’s Knob, Indiana, had only thirty seven registered automobiles, the mayor thought it would be safe to appoint his cousin, Henry Stables, who was the town cutup, as its traffic commissioner. But he soon regretted his decision. When the town awoke one morning, it found that a profusion of signs had been erected establishing numerous one way streets and confusing restrictions on turns.

The citizens were all for tearing down these signs until the police chief, another cousin of the mayor, made a surprising discovery. Motorists passing through town became so exasperated that sooner or later they made a prohibited turn. The police chief found that the town was making even more money from these traffic violations than from its speed trap on an outlying country road.

Of course everyone was overjoyed, particularly because the next day was Saturday and Moses McAdam, the county’s richest farmer, was due to pass through the town on his way to the county seat. They expected to extract a large fine from Moses, believing it to be impossible to drive through town without at least one traffic violation. But Moses had been secretly studying the signs. When Saturday morning came, he astonished the entire town by driving from his farm through town to the county seat without a single violation!

Can you discover the route Moses took? At each intersection you must follow one of the arrows. That is, you may turn in a given direction only when there is a curved line in that direction, and you may only go straight only when there is a straight line to follow. No turns may be made by backing a car around a corner. No U-turns are permitted. You may leave an intersection only at the head of an arrow. For instance, at the first intersection after leaving the farm, you only have two choices: to go north or to go straight (East). If you go straight (East), at the next intersection you must go either straight (East) or turn South. True, there is a curved line to the North, but there is no arrow pointing North, so you are forbidden to leave that intersection in a northerly direction.”

You can send in your answers by typing in N, S, E, W (North, South, East, West) at every intersection.

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Have an a-maze-ing week ahead!

 

Posted in Puzzles | Tagged , | 1 Comment

Solution To Puzzle #138: Traffic in Floyd’s Knob

I loved this puzzle so much that I ended up putting the original picture for the puzzle, not realising that the one Martin Gardner had put in his book was a different one, and therefore some of the description of the puzzle was not matching the picture, as pointed out by Suman Saraf – thanks Suman! Anyway, the puzzle still was a valid one. I only received two correct solutions – Suman Saraf and from my niece, Radhika Goyal. Well done both!

It was not an easy puzzle. The trick, at least for me, was to try it both backwards and forwards and find a meeting path. Here is a solution to the puzzle:

E,E,E,S,S,S,E,N,N,N,N,W,W,S,S,E,E,S,S,W,W,W,N,N,N,W,S,S,S,E,E,N,W,W,N,N,E,S,S,E,E,E,E

It might be easier to see the video as the answer, link attached here:

 

Hope you all enjoyed the puzzle!

 

Posted in Solution | Tagged , | Leave a comment

Puzzle #139: Gold Links

This is another famous puzzle in the Martin Gardner collection, and variations of this puzzle exist in different “sizes”. This particular one has been picked up from The Colossal Book of Short Puzzles and Problems, Puzzle 9.18. Replicating the puzzle as is.

Lenox R. Lohr, president of the Museum of Science and Industry in Chicago, was kind enough to pass along the following deceptively simple version of a type of combinatorial problem that turns up in many fields of applied mathematics. A traveler finds himself in a strange town without funds; he expects a large check to arrive in a few weeks. His most valuable posession is a gold watch chain of 23 links. To pay for a room he arranges with a landlady to give her as collateral one link a day for 23 days.
Naturally, the traveler wants to damage his watch chain as little as possible. Instead of giving the landlady a separate link each day he can give her one link the first day, then on the second day take back the link and give her a chain of two links. On the third day he can give her the single link again and on the fourth take back all she has and give her a chain of four links. All that matters is that each day she must be in possession of a number of links that corresponds to the number of days.
The traveler soon realizes that this can be accomplished by cutting the chain in many different ways. The problem is: What is the smallest number of links the traveler needs to cut to carry out his agreement for the full 23 days? More advanced mathematicians may wish to obtain a general formula for the longest chain that can be used in this manner after n cuts are made at the optimum places.

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy gold digging!

Posted in Puzzles | Tagged , | 5 Comments

Solution to Puzzle #137: The Burning Island

As I mentioned, this was an untypical problem, and I did not get as many responses 😦 The ones who responded correctly included Girish Tutakne, Suman Saraf and Neeraj Aggarwal+Anisha Goyal as a team over the lunch table!

Solution is as follows:

The man picks up a piece of wood and lights it from the fire on the west end of the island.

He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area.

The man survives the fire, but dies of starvation, with all the food in the forest burnt!

Hope you all enjoyed the puzzle.

 

Posted in Solution | Tagged , | Leave a comment

Puzzle #138: Traffic Flow in Floyd’s Knob

This is a very nice “maze” puzzle, borrowed from Martin Gardner’s book “The Colossal Book of Short Puzzles and Problems” Problem 10.14. The puzzle first appeared in 1962, in Martin Gardner’s Scientific American column. It was created by Robert Abbott, and in 1997 appeared in his book, SuperMazes.2 Thanks to Google, I was able to retrieve the original figure of this puzzle.

Puzzle 138 Graphic

Puzzle 138 Graphic

Here is the original story with the puzzle:

“Because the town of Floyd’s Knob, Indiana, had only thirty seven registered automobiles, the mayor thought it would be safe to appoint his cousin, Henry Stables, who was the town cutup, as its traffic commissioner. But he soon regretted his decision. When the town awoke one morning, it found that a profusion of signs had been erected establishing numerous one way streets and confusing restrictions on turns.

The citizens were all for tearing down these signs until the police chief, another cousin of the mayor, made a surprising discovery. Motorists passing through town became so exasperated that sooner or later they made a prohibited turn. The police chief found that the town was making even more money from these traffic violations than from its speed trap on an outlying country road.

Of course everyone was overjoyed, particularly because the next day was Saturday and Moses McAdam, the county’s richest farmer, was due to pass through the town on his way to the county seat. They expected to extract a large fine from Moses, believing it to be impossible to drive through town without at least one traffic violation. But Moses had been secretly studying the signs. When Saturday morning came, he astonished the entire town by driving from his farm through town to the county seat without a single violation!

Can you discover the route Moses took? At each intersection you must follow one of the arrows. That is, you may turn in a given direction only when there is a curved line in that direction, and you may only go straight only when there is a straight line to follow. No turns may be made by backing a car around a corner. No U-turns are permitted. You may leave an intersection only at the head of an arrow. For instance, at the first intersection after leaving the farm, you only have two choices: to go north or to go straight (East). If you go straight (East), at the next intersection you must go either straight (East) or turn South. True, there is a curved line to the North, but there is no arrow pointing North, so you are forbidden to leave that intersection in a northerly direction.”

You can send in your answers by typing in N, S, E, W (North, South, East, West) at every intersection.

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Have an a-maze-ing weekend!

 

 

Posted in Puzzles | Tagged , | Leave a comment

Solution to Puzzle #136: Talkative Eve

This was not as difficult a puzzle as it appeared to be, though required some work! Was glad to see most of the regular puzzlers answer this, which included Karan, Abhinav Jain, Suman Saraf, Girish Tutakne and Ruchir Godura (welcome back!).

I am taking the liberty of reproducing Karan’s answer:

We’ll proceed after reducing it to the following form.
(EVE/DID)*9999=TALK
Now 9999 has the following prime factors 3,3,11,101 out of which possible 3 digit numbers with similar first and last digits are 101, 303 and 909. 101 can be ruled out as value of the fraction is less than 1 and 101 is the smallest number of the above mentioned form.
9999/909=11, when EVE*11 the last digit would be E which is not the case, hence 909 can also be rejected. Which leaves us with 303=DID.
The options for EVE are 1?1, 2?2 (?=[0,9])
1?1 can be rejected as 1?1*33 will leave K=3 which contradicts D=3.
We’re now left with 212, 242, 252, 262, 272, 282, 292.
We now know for sure that K=6 so all we have to check is 212,242,252,272,282,292.
242/303= .79867986….

hope you all enjoyed the puzzle!

Posted in Solution | Tagged , | Leave a comment

Puzzle #137: Burning Island

For a change, this one is not a mathematical puzzle, but a nice logic puzzle (and there is no play of words here). I took this one from mathsisfun.com

A man is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the man survive the fire? (There are no buckets or any other means to put out the fire)

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy fire fighting!

Posted in Puzzles | Tagged , | 3 Comments

Solution to Puzzle #135: Two Dice = Nine Cards

This was a beautiful puzzle and only a few people sent correct answers. Only Suman Saraf sent the correct answer – fantastic job, this was a tough one – hats off to you!

Gurmeet.net, the place I took the solution from, has the answer, but not the method to arrive at the answer. Google came to my rescue and I found some other sources. The answer is indeed beautiful and in the end, it is just use of simple logic in the end.

Here is the answer – the cards will have the following numbers:

0.5,1.5,2.5,2.5,3.5,4.5,4.5,5.5,6.5

Here is the proof I have borrowed from http://puzzling.stackexchange.com/questions/25457/two-dice-nine-cards:

Solution to Puzzle #135

Solution to Puzzle #135

Hope you all enjoyed the puzzle!

 

Posted in Solution | Tagged , | Leave a comment