Logic & Reasoning – Top Level Problems
Prompt: Given the four overlapping circles at right, arrange the numbers
1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in each of the of the regions formed by the circles so that
the sum of numbers in each circle is the same.
Answer:
8
3
4
6
7
2
10
1
5
9
Source: University of Northern Colorado Mathematics Contest
Prompt: Who’s On First??
On the basis of the information provided below, determine who plays what position. There are 9
positions and one player sits on the bench. Also, assume a bachelor implies no children. Finally
“battery” means the pitcher and the catcher.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
Andy dislikes the catcher.
Ed’s sister is engaged to the second baseman.
The center fielder is taller than the right fielder.
Harry and the third baseman live in the same building.
Leroy and Allen each won $20 from the pitcher at pinochle.
Ed and the outfielders play poker during their free time.
The pitcher’s wife is the third baseman’s sister.
All the battery and the infield, except Allen, Harry, Andy, are shorter than Sam.
Leroy, Andy, and the shortstop lost $150 each at the racetrack.
Leroy, Harry, Sean, and the catcher took a trouncing from the second baseman at pool.
Sam is undergoing a divorce suit.
The catcher and the third baseman each have two children.
Ed, Leroy, Jerry, and the right fielder and center fielder are bachelors; the others are
married.
n. The shortstop, the third baseman, and Sean each won $100 betting on the fights.
o. One of the outfielders is either Mike or Andy.
p. Jerry is taller than Sean; Mike is shorter than Bill. Each of them is heavier than the third
baseman.
Prompt: “How old are your three children?” the mathematics teacher asks a former
student. He is told their ages add to 13 and multiply to give the number of his
classroom door (which they both can see). “I will need to know more,” the teacher
says, after a few moments reflection. He is told that the eldest child is learning to play
the violin. After this the teacher knew the 3 ages. What are their ages?
Answer: 2, 2, 9
Math’s Mate Gold, J.B. Wright, 1995
Prompt:
This year, Col. Mustard and the other five clue suspects spent their holidays in a
different country (three spent their holidays in Europe in Austria, Norway, and Scotland,
in some order; one in Argentina, one in New Zealand, and one in South Africa). While
on holiday, each happened to run into a famous movie star, one of whom was Meg
Ryan. Each suspect, being a fan of the particular star with whom he or she met,
desperately wanted an autograph, but not having a piece of nice paper handy, each got
the star’s autograph on a different item - in an address book, on the flap of an envelope,
on the back of a losing lottery ticket, on a napkin, a shirt sleeve, and even on a white hat
one was wearing!
From the clues, determine the country where each suspect spent his or her holiday, the
star each encountered, and where each star wrote his or her autograph. NOTE: in this
problem, an actor refers to a male star and an actress to a female star.
1. Mrs. Peacock didn’t get an autograph on her napkin while dining in a restaurant.
2. Julia Roberts was visiting in Norway and was very gracious when asked for her
autograph.
3. Prof. Plum, who vacationed in Europe, is not the suspect who got an autograph on
the back of an old losing lottery ticket that somehow had not made it into the trash.
4. Brad Pitt is the movie star who signed one of the suspect’s white hat.
5. The suspect who visited New Zealand (who wasn’t Mrs. White) was thrilled when
Harrison Ford signed their napkin.
6. The suspect visiting Scotland over the holidays went home to the States with an
autograph of Tom Selleck.
7. Miss Scarlet had a nice visit with the actor she met that signed the flap on an old
envelope.
8. The suspect who visited Austria (who wasn’t Mrs. White) ended up with the
autograph of one of the actresses in her address book.
9. Mr. Green, who spent his holidays in either Argentina or New Zealand, was thrilled
when he got Melanie Griffin’s autograph.
Answer:
Col. Mustard, New Zealand, Harrison Ford, napkin
Miss Scarlet, Scotland, Tom Selleck, flap of envelope
Mr. Green, Argentina, Melanie Griffin, old lottery ticket
Mrs. Peacock, Austria, Meg Ryan, address book
Mrs. White, South Africa, Brad Pitt, white hat
Prof. Plum, Norway, Julia Roberts, shirtsleeve
Brad Avery, 2004
Prompt: When asked about the ability of her cats to catch rats, Miss Kitty replied, “On
average, we find a cat-and-a-quarter can catch a rat-and-a-quarter in a minute-and-aquarter.” How many rats could ten of these cats catch in ten minutes?
Answer: 80
Math’s Mate Gold, J.B. Wright, 1995