Transcript 5-Minute Check - Cardinal Newman

A Question…
I’m thinking of a number…
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A Question…
I’m thinking of a number…
It’s 54!
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Example
Three brothers each arranged to spend an evening with a woman that he
had never met before. Each wanted to show off how suave and debonair
he could be, so each formed a plan.
By coincidence, each brother decided to buy a box of candy at the same
store, and each bought tickets at the same ticket outlet.
When it came time to leave, each brother grabbed the wrong candy box
and ticket envelope. None of them took the candy or the tickets that
belonged to him. Each took the tickets of one brother and the candy of the
other. Andy didn’t have Marty’s candy…you figure out the rest.
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Another Example
Penny’s favorite coin is the dime. Since we last saw Penny, she has spent
some of her dimes and has acquired some more. She doesn’t know how
many she has now, but she knows she has fewer than 100. One day she
was arranging them on her desk in different ways. She found that when she
put them into piles of 2, there was 1 left over. When she put them into piles
of 3, again there was 1 left over. The same thing happened when she put
them into piles of 4. She then tried putting them into piles of 5 and found
that there were none left over. How many dimes does Penny have? (There
is more than one correct answer).
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Another Methodology
Proof by contradiction – Indirect Proof
We make an assumption and then look for
an occasion where it is not true.
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Example
Jim tells lies on Fridays, Saturdays, and Sundays. He tells
the truth on all other days. Freda tells lies on Tuesdays,
Wednesdays, and Thursdays. She tells the truth on all other
days. If they both say, “Yesterday I lied,” then what day is it
today?
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Cryptarithms
Emil and Olive live on a farm with their
father, Gordon. One day Emil asked his
father, “Dad, what happened to that cat we
used to have?” Olive overheard this and
said, “Yeah, and we used to have a horse
too.” Gordon replied, “That tomcat and that
old nag were no use. I traded them for our
new goat.”
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Cryptarithms…Continued
Emil said, “Hey, that sounds like a good cryptarithmetic
problem. Come on Olive, let’s see if we can solve it. Each
letter stands for a different digit, 0 through 9. No two letters
stand for the same digit.
T O M
+
N A G
G O A
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Another Example
Seymour sells his Sausage and Meatball Combo to
2 Fast Stop stores and one Circle B store. After an
accident, he can’t remember which streets the
stores are on. What he does know is that the
streets are numbers from 1st Street up to 154th
Street, and he remembered that the two Fast Stop
stores were on streets whose numbers added up to
50. He also remembered that the Circle B store
was two streets away from one of the Fast Stop
stores. And he remembered that he called the
Sausage and Meatball Combo his “prime” favorite
because all three stores were on prim-numbered
streets. He didn’t have enough information yet…
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We Continue
He called his friend Gus and Gus could remember only the
last digit of the product of the numbers of the streets the
stores were on. Find the street numbers.
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Homework
Page 68, 1-8 all
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