Logic Puzzles

June 7, 2013


1. The Missing PieceBelow the four parts have been reorganized. The four partitions are exactly the same in both arrangements. Why is there a hole?
Where does this hole come from?
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2. Four GallonsYou have a three gallon and a five gallon measuring device. You wish to measure out four gallons.
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3. The IslandersThere are two beautiful yet remote islands in the south pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands, and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same Island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?
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4. Five GallonsYou are mixing cement and the recipe calls for five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four gallon bucket and a seven gallon bucket and nether has graduation marks. Find a method to measure five gallons.
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5. Two StringsYou have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.
How do you measure 45 minutes?
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6. The CubesA corporate businessman has two cubes on his office desk. Every day he arranges both cubes so that the front faces show the current day of the month.
What numbers are on the faces of the cubes to allow this?
Note: You can’t represent the day “7” with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be “07”.
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7. The Pot of BeansA pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans.
A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what color, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.
At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What color is it?
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8. The PigeonTwo friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.
How many miles does the pigeon travel?
Guess:  Guess | Show Hint Show Solution

9. The SocksThere is a lightbulb (incandescent, it’s currently off) in an upstairs room. You are downstairs, standing next to a panel of three light switches (all of them in the off position). One of them controls the lightbulb. The other two don’t do anything. You must figure out which switch controls the bulb, with some restrictions.
1) You can do whatever you want to the lightswitches, as long as it’s either turning them on or turning them off.
2) After fiddling with the lightswitches, you can go upstairs and check the bulb.
3) You cannot see the bulb nor any light shining from it from where you’re initially standing.
4) You cannot make multiple trips up and down the stairs.
5) The lamp is in the ceiling and you don’t have a ladder.
6) You are a mutant with 15-foot-long arms, so #5 is moot.
So, you fiddle with the switches, you walk upstairs and check the bulb, and then you immediately decide which switch controls the bulb.
How do you do it?
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1. The CamelsFour tasmanian camels traveling on a very narrow ledge encounter four tasmanian camels coming the other way.
As everyone knows, tasmanian camels never go backwards, especially when on a precarious ledge. The camels will climb over each other, but only if there is a camel sized space on the other side.
The camels didn’t see each other until there was only exactly one camel’s width between the two groups.
How can all camels pass, allowing both groups to go on their way, without any camel reversing?Show Hint Show Solution

2. The WaiterThree men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.
The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.
Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14…..where has the other $1 gone from the original $15?
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3. The Boxes

There are three boxes. One is labeled “APPLES” another is labeled “ORANGES”. The last one is labeled “APPLES AND ORANGES”. You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.

How can you label the boxes correctly?
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4. The CannibalsThree cannibals and three anthropologists have to cross a river.
The boat they have is only big enough for two people. The cannibals will do as requested, even if they are on the other side of the river, with one exception. If at any point in time there are more cannibals on one side of the river than anthropologists, the cannibals will eat them.
What plan can the anthropologists use for crossing the river so they don’t get eaten?
Note: One anthropologist can not control two cannibals on land, nor can one anthropologist on land control two cannibals on the boat if they are all on the same side of the river. This means an anthropologist will not survive being rowed across the river by a cannibal if there is one cannibal on the other side.
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5. The FatherA mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.
Where’s the father?
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6. The Double Jeopardy DoorsYou are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don’t know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth ,the other always lies and you don’t know which is which.
What is the question you ask?
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7. The FrogA frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?
Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.
Guess:  Guess | Show Hint Show Solution

8. The BobberYou can paddle your canoe seven miles per hour through any placid lake. The stream flows at three miles per hour. The moment you start to paddle up stream a fisherman looses one of his bobbers in the water fourteen miles up stream of you.
How many hours does it take for you and the bobber to meet?
Guess:  Guess | Show Hint Show Solution

9. The SocksCathy has twelve black socks and twelve white socks in her drawer.
In complete darkness, and without looking, how many socks must she take from the drawer in order to be sure to get a pair that match?
Guess:  Guess | Show Solution

10. There is something about MaryMary’s mum has four children.
The first child is called April.
The second May.
The third June.
What is the name of the fourth child?
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11. Petals around the roseThe name of the game is Petals Around the Rose, and that name is significant. Newcomers to the game can be told that much. They can also be told that every answer is zero or an even number. They can also be told the answer for every throw of the dice that are used in the game. And that’s all the information they get.
The person who has the dice and knows the game, rolls five dice and remarks almost instantly on the answer. For example: in Roll #1 the answer is two.
Roll #1. 4 1 6 3 6
“The answer is what?” says the new player.
“On that roll?”
“Would it still be two if I moved the dice without turning any of them over, just rearranging the pattern?”
“I can tell you only three things: the name of the game, the fact that the answer is always even, and the answer for any particular throw. In this case the answer is two.”
“So that’s how it is. What am I supposed to do?”
“You’re supposed to tell me the answer before I tell you. I’ll give you all the time you want, but don’t tell me your theory, just the answer. If you figure it out, you don’t want to give the idea away to these other jokers around you. Make them work for the answers, too. If you get the answer right on six successive rolls, I’ll take that as prima facie evidence that you understand the game.”
“OK, roll again.”
Roll #2. 5 6 5 4 4
“I give up. What’s the answer?”
“The answer is eight.”
“Roll again.”
Roll #3. 3 5 5 5 6
The answer is fourteen.
Roll #4. 2 6 2 1 4
The answer is zero.
Roll #5. 4 3 2 1 3
The answer is four.
Roll #6. 6 5 6 2 2
The answer is…  Guess |
An integral part of the puzzle is that those who have solved it are urged to keep the solution a secret, so there is no solution posted here. It is not a hard puzzle to figure out however.
A claim that often accompanies these instructions is that the smarter an individual, the greater amount of difficulty the individual will have in solving it. If such a statement is true, it may be attributed to the fact that “smarter” people tend to be more knowledgeable in a wide range of information which they may unnecessarily attempt to draw upon to solve the puzzle.

Well the yanks finally did it.

Five years and nine months after trading Alfonso Soriano for Alex Rodriguez in February of 2004, their master plan of winning the World Series and avenging their defeats at the hands of first the Arizona Diamondbacks in 2001 (Curt Schilling, Randy Johnson) and then the Florida Marlins in 2003 (Josh Beckett) finally came to fruition.

Well, not exactly. There were some weird detours in the road.

First, in 2004, they ALMOST got there. they hung a 3-0 lead on the Boston Red Sox in the ALCS–and you know the rest. They caved, the choked, they lost four straight–the only team in baseball history to do that–and the Red Sox reversed the curse and won the world series in 2004.

In 2005, the Yanks lost to the Angels in the AL Division Series. This was pretty awful. The Angels didn’t even make it to the Series–the White Sox did, and the White Sox won and reversed their Curse and won the series against the Houston Astros, which appeared in the series for the first time.

In 2006, the Yanks tried again. This time, they were destroyed by the Detroit Tigers 3-1 in the ALDivision Series, but at least the Tigers got to the World Series. But the Tigers, who had great pitching and Jimmy Leyland as manager, lost to the St Louis Cards and Tony LaRussa. That was a real upset, since the Cards had won only 83 games all season long.

In 2007, the Cleveland Indians, with a couple of guys named Cliff Lee and CC Sabathia, knocked the Yanks out of the AL Division Series for the third year in a row, 3-1. The Red Sox edged the powerful Indians 4-3 in the ALCS (which was probably the real world series) and then went on to sweep the hapless Colorado Rockies 4-0, who were probably just happy to be making their first appearance in world series play.

So now, since AROD had arrived, the yanks had 1) made one of the all time chokes in alcs history in 2004, and 2) lost three straight ALDS series for the first time in who knows when…

Did they trade A-ROD? of course not..they fired Joe Torre instead…

and in 2008, the Yankees missed the playoffs entirely, while the tampa bay rays (they took the name devil out, pleasing god) and the red sox took the two playoff spots in the al east. tampa disposed of the white sox while boston beat the angels, and then tampa got rid of the red sox in a great seven game alcs.

meanwhile, the phillies, who had edged out the mets in 2007 to win the nl east, only to be swept out in the nlds by the rockies, won the nl east again in 2008, and this time, they took care of business, beating the Brewers with cc sabathia, and then meeting–the la dodgers with joe torre as manager.

so in 2008 joe torre got to the playoffs but a rod did not.


the dodgers played the phils tough but the phils won in 5 in the nlcs, setting up a great world series, which was dominated by cole hamels and brad lidge’s great pitching.

Those scores, if you recall, were;
g1 philly 3-2
g2 tampa 4-2
g3 philly 5-4
g4 philly 10-2
g5 philly 4-3

notice that this was a low-scoring series with 3 one run games and a two run game and only one blowout? both tampa bay and the phillies had great pitching, great fielding, great speed, and great defense.

This year, the yanks decided to get drastic. they opened their wallets and bought;
1) cc sabathia
2) aj burnett and
3) mark teixeira

well, these were wise investments. the yanks won 103 games with these three guys, and blew through the playoffs to the world series.

burnett won one key game in the series. sabathia was solid in two games of the series, even if he lost game one. teixeira was an animal who had to be pitched around even if he wasn’t great, so a rod got more pitches to hit.

but as great as this team now is, there’s a big problem.

it took them so long to get here, the core is old.

1 C Jorge Posada# 37
4 SS Derek Jeter 35
5 3B Alex Rodriguez 33
6 LF Johnny Damon* 35
9 DH Hideki Matsui* 35
11 C Jose Molina 34
23 P Andy Pettitte* 37
24 P A.J. Burnett 32
29 P Mariano Rivera 39

Nick Swisher is 28, and Mark Teixeira is 29, so actually they might be expected to decline in the years ahead.

But clearly, athletes after age 27 or 28 have age related declines, and athletes after age 35, have sharp age related declines and are subject to career ending injuries.

The yankees are simply not just old, they are geriatric at five key batting positions, and three key pitching positions.

They also lack a #4 and a #5 starter, and lack depth in the bullpen.

Melkey Cabrera can’t field, and he can’t hit.

Hideki Matsui is a free agent in any case, and wants to go to the west coast by all accounts. He wants a lot more money.

CC Sabathia is 28, but let’s face it, the man looks like he lives on a diet of pizza and philly cheesesteaks. when i told my kids he was 28, my daughter, who is 15, remarked, “he looks like he’s 45” or something like that.

pitchers with cc sabathia’s build and body type don’t tend to age well, and do tend to come down with arm problems, as opposed to pitchers with cole hamels or cliff lee’s body type.

for example, brett myers has always been overweight. this is one of the reasons he’s been injury prone his whole career. a pitcher needs to be light and have good mechanics to stay healthy over the course of a season.

cliff lee has beautiful mechanics.

the good news for the yanks is they have a lot of good young pitchers who may mature into much better pitchers. i like their young staff and i believe that one or two or more of them will emerge as real winners next year–after all, they have a good offense behind them.

I should point out one last point–the sabrmetrician in me needs to. Although the Yankees won 103 and lost 59, their pythagorean won lost record was only 95-67, based on their scoring 915 runs and allowing 753 runs. That means that they won eight more games than they should have based on random or luck factors–regression to the mean would suggest that they are actually a 95 win ball club that got a bit lucky this year. They did have a 22-16 record in one run games, which perhaps explains some of this disparity. Also, the Yanks were 7-3 in extra inning games as well.

But those kind of results tend to even out over seasons.

Assuming they regress back to 95 wins, and lose 7-8 wins off of that due to age or related factors, the yankees might not even get back to the playoffs in 2010.

The Yankees to get back, need to retool, get younger, and address their serious aging problem.

I will address the Phillies in a separate article.

In the meantime, the Yankees and their fans should enjoy their parade. It’s very likely the last hurrah of a great core that has now won five world championships in 14 seasons since 1996, and appeared in seven world series during that time, just about half of them. It’s a truly remarkable achievement.

Jeter, Rivera, Posada, Bernie Williams, Andy Pettite, all now seemed bound to cash in their ticket for the Hall of Fame.

Alex Rodriquez has tainted credentials due to steroid use. I personally would not vote for him, or any other steroid user. At least I would take a wait and see attitude on those guys. Roger Clemens, who was a key part of several of those teams, is also now a problem child due to steroid allegations, but Clemens is also clearly perhaps the greatest pitcher who ever took the mound, so he’s kind of a borderline issue case, whereas Rodriguez is kind of like Vern Stephens on steroids.

So hats off the yanks, and make sure their medicaid cards and long term care policies are paid for.

–art k philly
home of Mr. November, Chase Utley
Home of the 2008 World Champion Phillies
“it was a very good year” –frank sinatra