







A four person race 
20191119 

From Juvy: 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? Answered by Penny Nom. 





Squares and rectangles 
20170715 

From Tront: 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. Answered by Penny Nom. 





Proof that an erroneous algebraic statement is false 
20151214 

From Berteanu: 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? Answered by Penny Nom. 





A problem in logic 
20120119 

From Ghader: 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? Answered by Robert Dawson. 





12 coins 
20100707 

From Eden: 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. Answered by Stephen La Rocque and Tyler Wood. 





Frogs and kangaroos 
20090216 

From Jenny: 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? Answered by Penny Nom. 





An Euler diagram and a logic argument 
20080918 

From Regina: 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 Answered by Penny Nom. 





A puzzle about hats 
20080303 

From Sylvia: 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.) Answered by Penny Nom. 





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

From Tom: 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. Answered by Harley Weston. 





Two logic problems 
20071207 

From Grace: 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 Answered by Penny Nom. 





Who is lying? 
20060114 

From Diane: 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?
Answered by Penny Nom. 





A torus and a sphere 
20050327 

From Tony: Is it possible to shrink a torus into a sphere? Answered by Andrei Volodin and Penny Nom. 





Trading fish for bread 
20050225 

From Mike: 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? Answered by Penny Nom. 





Crossing a river 
20040909 

From Barb: 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 Answered by Penny Nom and Claude Tardif. 





Jo's books 
20030407 

From Miguel: 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? Answered by Penny Nom. 





NO REDHATTED DWARVES ALLOWED 
20030114 

From Dulce:
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
Answered by Claude Tardif. 





Three bags of marbles 
20021108 

From A student: 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 Answered by Penny Nom. 





8 squares from 12 sticks 
20021008 

From A student: If you have 12 sticks the same size, how do you make them into 8 squares? Answered by Claude Tardif. 





The community garden 
20020908 

From Michele: 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? Answered by Leeanne Boehm. 





20 men dig 40 holes in 60 days 
20020724 

From Lindsey: 20 men dig 40 holes in 60 days. So, 10 men can dig 10 holes in how many days? Answered by Penny Nom. 





Logico mathematical knowledge 
20020123 

From A teacher: How does young children's logico mathematical knowledge develop? Answered by Walter Whitely. 





Who owns what pet? 
20011003 

From A parent: 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. . . . Answered by Judi McDonald. 





Taking matches 
20010505 

From Mark: 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? Answered by Claude Tardif. 





P vs NP problem 
20010301 

From Roy: 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? Answered by Claude Tardif. 





Crossing the dessert 
20010129 

From Zach: 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? Answered by Claude Tardif. 





Derfs, Enajs and Sivads 
20010107 

From John and Norman: 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? Answered by Penny Nom. 





Transporting bananas 
20001018 

From Krystie: 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 Answered by Penny Nom. 





A proof that 1=2 
20000919 

From sporky: 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. Answered by Walter Whiteley. 





Selling chickens 
20000912 

From Rick: 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. Answered by Penny Nom. 





The Village of Truth 
20000510 

From Sean Pearson: 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 ? Answered by Harley Weston. 





Tennis doubles 
20000204 

From Brittany Allinson: 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? Answered by Penny Nom. 





Logic and mathematical logic 
19991006 

From Polly Mackenzie: What is the difference between logic and math logic? Answered by Walter Whiteley. 





Jose and Arthur 
19990926 

From Joel Hammer: 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? Answered by Denis Hanson. 





Bales of hay 
19990913 

From Ivy: 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? Answered by Harley Weston. 





The three jugs problem 
19990902 

From Kent Lane: 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. Answered by Chris Fisher. 





The Bellhop Problem 
19990829 

From Gerard O'Neill: 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? Answered by Harley Weston. 





Crossing the Bridge 
19990827 

From Debbie Walter: 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? Answered by Penny Nom. 





A 
19990502 

From Leah: 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? Answered by Penny Nom. 





An Implication 
19980927 

From Danielle Evans: 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 Answered by Chris Fisher. 





A Logic Problem 
19980607 

From Anthony Bacigalupo: 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).... Answered by Chris Fisher. 





Logic and Matrix Instruction 
19980424 

From Robin Booker: 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.... Answered by Harley Weston. 





Smith, Rodriguez and Jones 
19961107 

From Rafayel Ambartsumyan: 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? Answered by Penny Nom. 

