







A four person race 
20191119 

Juvy pose la question : Ben finished seven seconds ahead of Mike.
Noel finished three seconds behind of Sam.
Mike finished five seconds behind Noel.
In what order did the friends finish the race? Penny Nom lui répond. 





Squares and rectangles 
20170715 

Tront pose la question : So, there's a general rule that all squares are rectangles but not all rectangles are squares. Im trying to find a term that would describe this relationship. I've found that if all of A is B but not all B is A then I'd say that A is a subset of B, but is there a term that describes the relationship as a whole? I don't want to describe the components, I want to describe the relationship as a whole. Penny Nom lui répond. 





Proof that an erroneous algebraic statement is false 
20151214 

Berteanu pose la question : I need help with this proposition:
"It exists x a real number that for every y real number 5*x2*y*y=1
This is false.
Let x be from R.
And I need an y real number that 5*x2*y*y!=1
Please,could you help me? Penny Nom lui répond. 





A problem in logic 
20120119 

Ghader pose la question : The puzzle below I know the answer to; because someone told me! My question is: how could I answer it using logic, maths, etc. what field of inquiry does this kind of problem fall into?
Puzzle: You are in a room with two men: one is a compulsive liar and the other is a compulsive honest. There are two doors: one leading to heaven, the other to hell. The two men know which door leads to where. You want to go to heaven but are allowed only ONE question from one or the other of the two men. What would that question be?
[The question to ask, from either man, is: "if I asked the OTHER man which door leads to heaven, which door would he point?". You would then choose the other door.]
Has this answer got any basis in logic or maths at all? Robert Dawson lui répond. 





12 coins 
20100707 

Eden pose la question : We have 12 coins same in size and shape and also weight.
But among these, one coin which has same size and shape, but not in weight
and we can't know that this coin was lighter or heavier.
We must decide which coin was lighter or heavier among these 12 coins in
4 times of weighting with scale. Stephen La Rocque and Tyler Wood lui répond. 





Frogs and kangaroos 
20090216 

Jenny pose la question : Albert, Bernard, Charles, Daniel and Ellie play a game in which each is a frog or kangaroo. Frogs' statements are always false while Kangaroos' statements are alwas true. 1. Albert says that bernard is a kangaroo. 2. Charles says that Daniel is a frog. 3. Ellie says that Alvert is not a frog. 4. Bernard says that Charles is not a kangaroo. 5. Daniel says that Elie and Albert are different kinds of animals. How many frogs are there? Penny Nom lui répond. 





An Euler diagram and a logic argument 
20080918 

Regina pose la question : Use a Euler diagram to determine whether the following argument is valid or invalid.
No wizard can yodel
All lizards can yodel
No wizard is a lizard Penny Nom lui répond. 





A puzzle about hats 
20080303 

Sylvia pose la question : There were 4 people sitting in a row, truing to win $50.00 from a riddle.
The one in front was wearing a red hat.
The second from the front was wearing a blue hat.
The third from the front was wearing a red hat.
The last was wearing a blue hat and is blindfolded.
Each of them were informed that they are all wearing a hat,
the last person is blindfolded and that there are 2 red and 2 blue hats. If they can guess the
colour of their hat, then they win the prize.
There was a long silence, then one of them guessed the color of his hat correctly. Who was it?
and explain why.
(note that they can only see the person in front of them and are not allowed to turn around and
see behind them.) Penny Nom lui répond. 





Prove (p & ~q) v p = p 
20080212 

Tom pose la question : Prove (p & ~q) v p = p
Do I need to use the absorption law p v (p & q)=p? If yes,how do I cope with the NOT(~) in q?Thank you. Harley Weston lui répond. 





Two logic problems 
20071207 

Grace pose la question : 1. You are an archaeologist that has just unearthed a longsought triplet
of ancient treasure chests. One chest is plated with silver, one with gold,
and one with bronze. According to legend, one of the three chests is filled with
great treasure, whereas the other two chests house a maneating python that
can rip your head off. Faced with a dilemma, you then notice that
there are inscriptions on the chests:
Silver Chest  Treasure is in this Chest.
Gold Chest  Treasure is not in this Chest.
Bronze Chest  Treasure is not in the Gold Chest
.
You know that at least one of the inscriptions is true,
and at least one of the inscriptions is false. Which chest do you open?
(a) Silver (b) Gold (c) Bronze Penny Nom lui répond. 





Who is lying? 
20060114 

Diane pose la question : A business man was working in his home office when he realized he had left a fivedollar bill in the book he had been reading. He called his butler to bring him the book from the library. When he got the book, the bill was no longer there. He then questioned the maid and the butler. The maid remembered seeing the bill between pages 99 and 100 in a book to the left of a business book. The butler did not recall seeing the bill, but was sure the book was to the right of the business book, because to the left of it there was a statistics book. Who is lying?
Penny Nom lui répond. 





A torus and a sphere 
20050327 

Tony pose la question : Is it possible to shrink a torus into a sphere? Andrei Volodin and Penny Nom lui répond. 





Trading fish for bread 
20050225 

Mike pose la question : Byron lives where people trade goods they produce for other things they
need. He has some fish and wants to trade them for bananas. He finds
the following:
5 fish = 2 loaves of bread
6 oranges = 2 melons
1 loaf of bread = 1 banana and 3 oranges
4 loaves of bread = 14 oranges
How many bananas can Byron get with 5 fish? Penny Nom lui répond. 





Crossing a river 
20040909 

Barb pose la question : Nine men and two boys, trekking through the jungle, need to cross a river. They have a small inflatable boat and it's easy enough to row it across the river. The boat, however, can hold no more than one man or the two boys. How can they all get across? (Hint. suppose there was only one man and two boys) Does it make math sense and what would the answer be Penny Nom and Claude Tardif lui répond. 





Jo's books 
20030407 

Miguel pose la question : Jo announces, "I have more than 999 books." Jean says: "No Jo! You have fewer than 1,000 books." Mary says: "Jo has at least 1 book." Only one of these statements is true. How many books does Jo own? Penny Nom lui répond. 





NO REDHATTED DWARVES ALLOWED 
20030114 

Dulce pose la question :
There are 1000 dwarves in Dwarfland. Now as you know, dwarves are born with either red or white hats on. The dwarves in Dwarfland love to party. Every night, they all flock to the same club to dance the night away. One day, a sign is posted at the club: "NO REDHATTED DWARVES ALLOWED". A certain number of days pass, after which all of the whitehatted dwarves are in attendance,and none of the reds. How did the red hats know not to come? Assumptions:  The number of red and whitehatted dwarves need not be equal. There are at least 1 of each color.
 There are no reflections or mirrors in Dwarfland (i.e. the dwarves can't see the color of their own hat), and no dwarf can reveal through direct or indirect means the color of another dwarf's hat.
 There is NO COMMUNICATION among dwarves
 No whitehatted dwarf ever misses a night of partying
Claude Tardif lui répond. 





Three bags of marbles 
20021108 

A student pose la question : I have 3 bags of marbles 1 bag is labeled blue; 2nd bag is labeled red; 3rd bag is labeled blue & red all the bags are mismarked your job is to take one marble from 1 bag look at it and correctly label all the bags Penny Nom lui répond. 





8 squares from 12 sticks 
20021008 

A student pose la question : If you have 12 sticks the same size, how do you make them into 8 squares? Claude Tardif lui répond. 





The community garden 
20020908 

Michele pose la question : Bryce, Duanne, Juliana and Sonya share a 40ft by 48 ft rectangular portion of the community garden in the neighborhood. With this space each has their own rectangular garden plot. Bryce is the only one with a square plot. its are is 1/2 the area of Duanne's The area of Bryce's plot is 2/3 the area of Julianna's plot. Their plots have one side in common. Sonya's garden has an area twice that of Julianna's garden. What are the dimensions of each person's garden plot? Leeanne Boehm lui répond. 





20 men dig 40 holes in 60 days 
20020724 

Lindsey pose la question : 20 men dig 40 holes in 60 days. So, 10 men can dig 10 holes in how many days? Penny Nom lui répond. 





Logico mathematical knowledge 
20020123 

A teacher pose la question : How does young children's logico mathematical knowledge develop? Walter Whitely lui répond. 





Who owns what pet? 
20011003 

A parent pose la question : Don, Frank, Jenny, and Ken each come from one state, either Alaska, Maine, Montana, or Oklahoma. They each speak one primary language, either English, french, Russian, or Spanish. And they each have one of four pets, a chinchilla, a dog, a hamster, or a turtle. Figure out which language and what pet each of the four people have, using the following clues. . . . Judi McDonald lui répond. 





Taking matches 
20010505 

Mark pose la question : Two piles of matches are on a table. A player can remove a match from either pile or a match from both piles. The player who takes the last match loses. If there are two players, how should you play? Claude Tardif lui répond. 





P vs NP problem 
20010301 

Roy pose la question : What math journals would publish a proposed solution to the P vs NP problem when the work has been done by an amateur mathematician who has no degree in math? Claude Tardif lui répond. 





Crossing the dessert 
20010129 

Zach pose la question : An Explorer needed to make a 5 day trip across a dessert. Each man with him could carry exactly 3 days food and water. For one man how many men will it take to cross the dessert? Claude Tardif lui répond. 





Derfs, Enajs and Sivads 
20010107 

John and Norman pose la question : All Derfs are Enajs. Onethird of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derf nor Sivad? Penny Nom lui répond. 





Transporting bananas 
20001018 

Krystie pose la question : A farm has 45 bananas, a man has to take a truck and transport 15 bananas to a market that is 15 miles away. Every mile he travels, he must eat a banana. I have to get at least one banana to the market Penny Nom lui répond. 





A proof that 1=2 
20000919 

sporky pose la question : Why does the proof for 1=2 not work? x = 1 x^{2} = 1 x = x^{2} 1 = 2x (derivitive) 1 = 2(1) 1 = 2 ??? please tell me where the false logic is. Walter Whiteley lui répond. 





Selling chickens 
20000912 

Rick pose la question : A man raised chickens. He sold all but 8 of them. The first buyer bought 1/3 of all the chickens + 2/3 of a single chicken. The second buyer bought 1/3 of the remaining chickens + 1/3 of a single chicken. The third buyer bought 1/3 of the remainder + 2/3 of a chicken. How many chickens did the seller own before selling any? All chickens were alive and whole when the buyers received them. Penny Nom lui répond. 





The Village of Truth 
20000510 

Sean Pearson pose la question : Our teacher gave us a logic problem involving two villages: the village of truth, and the village of lies. The problem is in asking two guards the right question to gain entrance to the fenced compound the villages are in without being shot. Have you heard of this problem ? Harley Weston lui répond. 





Tennis doubles 
20000204 

Brittany Allinson pose la question : Cheri, Beth and Jacinta are daughters of Mr. Sullivan, Mr. Marchand, and Mr. Benoit. Four of these people are playing tennis doubles. Mr. Benoit's daughter and Mr. Sullivan are partners. Cheri's father and Mr. Marchand's daughter are also partners. There aren't any father/daughter combinations. Who is Cheri's father? Penny Nom lui répond. 





Logic and mathematical logic 
19991006 

Polly Mackenzie pose la question : What is the difference between logic and math logic? Walter Whiteley lui répond. 





Jose and Arthur 
19990926 

Joel Hammer pose la question : Jose can run around the track in 40 seconds. Arthur runs with Jose but in the opposite direction. They meet every 15 second. How long will it take Arthur to make one trip around the track? Denis Hanson lui répond. 





Bales of hay 
19990913 

Ivy pose la question : You are given 5 bales of hay. Two bales are weighed at a time, which equal the following weights: 110, 112, 113,114,115,116,117,118,120,121. What does each individual bale weigh? Harley Weston lui répond. 





The three jugs problem 
19990902 

Kent Lane pose la question : I wonder if you could help me figure out this secondary Discrete Math Problem. I cannot figure out where this comes from. Here's the question: You have three containers. Container 1 is a three (3) liter container. Container 2 is a five (5) liter container. Container 3 is an eight (8) liter container that is full of liquid. The goal is to get 4 liters in one of the containers. Stipulations: There are no marks on the containers to measure out the liquid. All you know is that 1 is 3 l., 2 is 5 l., and 3 is 8 l. full of liquid. Chris Fisher lui répond. 





The Bellhop Problem 
19990829 

Gerard O'Neill pose la question : Three fellows going to a Math Conference book into a motel. "That will be $30.00" says the bellhop. Each fellow gives $10.00 and they go off to their room. The manager enters and says "That was a $25.00 room. Go and give them $5.00 back." The bellhop heads off but thinks....."how am I going to split $5.00 between 3 fellows? Hey I will keep two dollars and give each guy a dollar." He does just that.......each fellow now paid $9.00 and the bellhop kept two. 3 X 9= 27 plus the bellhops two = $29.00 Where is the missing dollar? Harley Weston lui répond. 





Crossing the Bridge 
19990827 

Debbie Walter pose la question : If you have four people who need to cross a bridge in the dark with only one flashlight and only two of them can cross at a time and their speeds of crossing are as follows:  one person can cross it in one minute
 one person can cross it in two minutes
 one person can cross it in five minutes
 and the slowest person can cross it in ten minutes
what is the shortest amount of time it would take to get all four across the bridge? Penny Nom lui répond. 





A 
19990502 

Leah pose la question : a=b a^2=ab a^2+b^2=abb^2 (ab)(a+b)=b(ab) a+b=b b 2=1 why is this proof wrong? Penny Nom lui répond. 





An Implication 
19980927 

Danielle Evans pose la question : i am in my second year of math for the liberal arts and a problem has be terribly confused.. can you answer this [(p > q) ^ (q > p)] > (p <> q) is this an implication?? i would love to hear your answer thank you... danielle evans Chris Fisher lui répond. 





A Logic Problem 
19980607 

Anthony Bacigalupo pose la question : My name is Anthony Bacigalupo and I take Sequential ][ Math and am taking a practice regents. When doing a logic problem, I encountered the following statements, where I am trying to prove P ( I left out steps unrelated to the question).... Chris Fisher lui répond. 





Logic and Matrix Instruction 
19980424 

Robin Booker pose la question : I need assistance with instruction strategies to teach the construction of a matrix, solving a logic problem. Providing instruction in the construction of a simple matrix , no problem. However, I stumpted on this one. Five players were chosen as All Stars at the basketball banquet. Based on the following clues, find the player's name, team, uniform color and number of points scored.... Harley Weston lui répond. 





Smith, Rodriguez and Jones 
19961107 

Rafayel Ambartsumyan pose la question : On a train, Smith, Rodriguez, Jones are the fireman, brakeman, and engineer, but not in that order. Also aboard the train are three businessman who have the same names, a Mr. Smith, a Mr. Rodriguez, and a Mr. Jones. ..... Who is the engineer? Penny Nom lui répond. 

