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.

Last Week
Well, last week went pretty well as we got 3 out of 4 right. That wasn’t looking so good until Mike Shanahan, who I savaged in last week’s column, decided, after going up 14-0 on Seattle, to leave RG3 out there on one leg and see how injured the guy could get facing the best defense in the NFC.
We discussed last week Shanahan’s history of abusing QB’s and going one and done with guys not named Elway.  Last week was a classic batch of evidence of this.  Up 14-0, Shanahan only had to do one thing–sit RG3 on the bench and go with his competent backup and sit on the lead.  Instead, he left a hobbled, injured QB out there too long–who by the time they actually needed him to come back and get the lead in the 4th Quarter, was way too banged up to play.  Had Shanahan rested him for two and one half quarters, RG3 might have had enough for one last drive–or his backup could have gotten it going enough to keep the ‘Skins in the game.  
RGIII was left in last weeks game way too long by Mike Shanahan
Now the Seahawks march on, Pete Carroll is a genius, Shanahan is a ninny, RG3 may be out for 1/2 of next year, RG3 has LCL and possibly ACL damage that is severe to the same knee he destroyed once already in college, and Shanahan is directly responsible for aggravating the injury for leaving in the  kid in there after the kid worked hard in the first quarter to get a two TD lead.   If I’m a tort lawyer, I’m suing Shanahan for negligence.  I mean, c’mon.  
Oh, and by the way, another one and done for Shanahan.  See?  And another playoff win on the road for Carroll, who continues to show his playoff genius.  And makes my pick of last week look like brilliance.  Since I analyzed it as a case of Shanahan will beat himself and Carroll will take advantage.
Cincinnati was lackluster in losing to the Texans in the playoffs for the second year in a row (though I have to give a shoutout to our high school QB, Haverford School/Boston College and former NY Giant Michael Mayock, who was broadcasting that game and actually made it interesting).  Mayock does all of the draft analysis for NFL Network and is one of the best prepared and best NFL and college broadcasters in the game, and one of the greatest athletes I ever saw play high school football (he once dropped 26 points in a 12 year old hoops game that was about five minutes long).  Greatest line from Mayock:  the other broadcaster mentions that Arrian Foster runs like Marcus Allen, and Mayock immediately says “Hey, I played against Marcus Allen” and goes on to note the similarities and differences.
Marcus Allen, OJ, Jim Brown & Walter Peyton v. Adrian Peterson & Eric Dickerson
Thirty years ago this month I was living in LA, and my good friend E.N. was visiting from NYC, and we scored fifty yard line seats for the LA Raiders-NY Jets playoff game in balmy 70 degree weather.  You may remember that this was the game won by the Jets (barely) using Richard Todd at QB, and with their famous defensive combo of Gastineau and Temple’s own Joe Klecko.  Famous for the fact that until Rex Ryan came along, the Jets had not won a playoff game since that 1983 contest for a long, long time.  
Anyhow, Marcus Allen was in that game as a rookie, and not ten rows ahead of us was sitting then world famous actor and sports commentator Orenthal James “OJ” Simpson, a white Bronco ride still ten years away in his future, sitting with his beautiful blonde wife and an equally beautiful blonde on the other side of him.  During the entire game we (meaning the whole crowd) were peppering him with cries of “Juice, Juice”.  After all, we were in the LA Coliseum, the very place he had played college ball for USC, and he was watching his good friend Marcus Allen play ball.  
Marcus Allen USC and LA Raider HOF RB
It seems a long time ago, but this year some running back made an assault on Eric Dickerson’s 16 game rushing record of 2105 yards achieved in 1973 (Adrian Peterson with 2,097).  The only problem being, both Peterson & Dickerson did it in sixteen games, whereas OJ Simpson’s record of 2,003 yards, set in 1973, was achieved in fourteen games.  OJ averaged more than 143 yards per game, whereas Dickerson, in the longer season, averaged only 132 yards per game.  Meaning that had OJ played two more games, it’s pretty safe to say that OJ would have gained 2,289 yards in a sixteen game season.
No one since OJ has gained 2,000 yards in 14 games or less, and if OJ were playing today, he’s probably have already broken the 2,500 yard mark for a running back in a sixteen game season with a bye.  Remember, too, he set that record playing in Buffalo, outside, in the snow, without a bye week.  
OJ Simpson – the greatest RB of them all?
OJ had another year two years later in 1975 where he gained 1817 yards in a 14 games season and averaged 130 yards per game.  If he had played 16 games that year, he’d have rushed for 2,017 yards that year.  That would still be 5th on the all-time list today ahead of all but Dickerson, Peterson, and the famous 2000 yard seasons of Jamal Lewis & Barry Sanders.  
This was probably the OJ look that launched his “Naked Gun” film career
Lest we neglect the greatest RB of them all, Jim Brown played 1/2 of his career in a twelve game NFL season.  In 118 games he rushed for 12,312 yards and averaged over his career 104.3 yards per game.  In 1963, Brown rushed for 1863 yards and averages 133.1 yards per game, which means if he had played 16 games in 1963, he would have rushed for 2,129 yards.  
Needless to say, Jim Brown would have been the all-time rushing leader and the first to break the 2,000 yard barrier if he had played a 16 game season.  Moreover, Brown’s retrospective 2,129 yards he would have gained in 16 games played with a bye in 1963 would rank first in the NFL overall today, and would only rank behind OJ’s retrospective 2,289 yards which OJ would have carried in 1973 given sixteen games and a bye.
Consequently, let’s forget about Adrian Peterson and Eric Dickerson, who are great HOF backs, and concentrate on who were the greatest NFL running backs in history.  That list comes down to three–Jim Brown, OJ Simpson, and Barry Sanders.   And of course, the late Walter Peyton, whose 1977 season rushing for 1852 yards with a pace of 132 yards per carry in a fourteen game season would have propelled him to a total of 2,116 yards in a sixteen game, bye week season.  That would have ranked him third all time in NFL history.  
the late Walter Payton – perhaps the most beloved football player of all time
And I’d take Marcus Allen after them and before Eric Dickerson or Adrian Peterson.  Allen was as good a receiving back as he was a running back, and in his NFL career rushed for 12,000 plus yards as well as caught passes receiving for another nearly 5,500 yards at a nearly 10 yards per reception clip.  If you split him into two he’d be two HOFers, but as a single back, he was a wrecking crew.  In 1985 he totalled 2314 yards from scrimmage, 1780 on the ground and another 555 in reception yards.  Yikes.  Not even Sanders, Peyton, Simpson or Brown were that versatile.  Peyton could catch and run with the ball more than the others–and Sweetness was truly great–but at his peak, Marcus Allen literally destroyed defenses.  
In the Super Bowl of January 1984 between the LA Raiders and the Washington Redskins, wherein the Raiders destroyed the Redskins 38-9, Marcus Allen rushed for 191 yards on 20 rushing attempts.  John Riggins on the other side only gained 64 yards on 26 attempts.  The combination of Marcus Allen and Jim Plunkett was, literally, unstoppable, and the Raiders crushed a Washington Redskins team that had won the Super Bowl the very previous year over Dan Marino and the Miami Dolphins.  They didn’t just beat the Redskins–they destroyed, humiliated and made a laughingstock of them, so much so that everyone forgot that the Redskins had ever been champions the year before.  
Marcus Allen’s 9.55 yards per carry Super Bowl rushing average is second all time in Super Bowl history–to the immortal Tom Matte of Baltimore, who averages 10.55 yards per carry back in Super Bowl III (which the Jets, not the Colts won).  Matte rushed for 116 yards on 11 attempts in that game, but that was in a losing effort.  Matte and Unitas were usually a terrific pair, but Namath and his teammates were just better that day–a lot better.  
That was how good Marcus Allen was.  And as good as OJ, Peyton, Jim Brown, and all the rest were, only Walter Peyton won a Super Bowl, and Jim Brown an NFL championship.  Marcus Allen didn’t just win a Super Bowl–he dominated it.  
Saturday’s Games:
Baltimore Ravens at Denver Broncos:
I’m getting this out a little late, so really I shouldn’t be picking so late on this one, but I’m going with the conventional wisdom and picking Denver, at home, over Baltimore.  Ave atque value, Ray Lewis.  Those about to do NFL combat for the last time salute you, you are a true warrior.  
Green Bay Packers at San Francisco 49ers:
This is a very close matchup.  Green Bay has a better offense with Aaron Rodgers, but SF has a superior defense, and one has to like the Niner’s coaching scheme.  Also, the Niners have the home field, which is a big difference from playing on the frozen tundra of Lambeau Field.  I like the 49ers in a close game.  
Sunday’s Games:
Seattle Seahawks at Atlanta Falcons:
On paper, you’d have to like the Seahawks.  However, Atlanta is very tough at home, they have the bye week, and Matt Ryan is a much more veteran and savvy QB than rookie RGIII, and will play for the long haul.  Atlanta has a good rushing attack with Turner and Rodgers to go with the passing attack of Ryan, and Atlanta also has an excellent defense.  Think about Atlanta’s 34-0 smackdown of the NY Giants in the Dome, and you get the idea of how good Atlanta can play at home, and their 13-3 record is nothing to sneeze about.  I pick Atlanta.
Houston Texans at NE Patriots:
This is a rematch of last year’s playoff game, wherein the Patriots pretty much destroyed the Texans.  As much as one would like to see a different result, the fact is that Tom Brady and the Pats are really good at home, they scored the most points of any team in the league, and their defense is pretty darn good also.  And their QB is very good.  The Texans won last week, but in one of the most boring games ever, and other than Arrian Foster, they just don’t have the offensive weapons to keep up with the Patriots, and their defense will not shut down Tom Brady for an entire game–the Patriots scored 557 points this season.  
The Canton Bulldogs, which featured Jim Thorpe, and played in the NFL only during the 1920s (my late grandfather lived in Canton OH for two years and watched Jim Thorpe play football), won two NFL championship.  That is more NFL championships than the Seattle Seahawks, the Houston Texans, the Jacksonville Jaguars, the Carolina Panthers, the Atlanta Falcons, the Cincinnati Bengals, the Minnesota Vikings (all of which have zero NFL or Super Bowl championships), and more than the Baltimore Ravens, the New Orleans Saints, the Tampa Bay Bucs, the NY Jets or the San Diego Chargers (all of which have one Super Bowl or NFL/AFL championship).  The Broncos, Bills, Chiefs, Titans, Dolphins and most embarassingly, since they’ve been in the league since 1920, the Chicago/St Louis/Arizona Cardinals, are all tied with Canton with two championships.   So much for NFL parity.  18 teams have won the same number or fewer NFL championships as the Canton Bulldogs, a team that last played during the Coolidge Administration.  Even the Philadelphia Eagles have three NFL championships (1948, 1949 and 1960).  
Art Kyriazis, Philly


Arthur John Kyriazis Google Blog: Easter 1916 William Butler Yeats.