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1) Sally invited 17 guests to a dance party. She assigned each guest a
number from 2 to 18, keeping 1 for herself. The sum of each couples
numbers was a perfect square. What was the number of Sally's partner?
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2) There is a series of nine numbers: 3, 3, 5, 4, 4, 3, 5, 5, 4, __
followed by a blank. What's the blank, and why?
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3) Suppose you're on a game show, and you're given the choice of three
doors: Behind one door is a car; behind the others, goats. You pick
a door, say No. 1, and the host, who knows what's behind the doors,
opens another door, say No. 3, which has a goat. He then says to
you, Do you want to pick door No. 2; Is it to your advantage to
switch your choice? Why?
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4) If x = 1 and y = 1 then: x = y
Multiplying each side by x gives us: x^2 = xy
Subtracting y^2 from each side gives us: x^2-y^2 = xy-y^2
Factoring each side gives us: (x+y)(x-y) = y(x-y)
Dividing out the common term (x-y) gives us: x+y = y
When we put the initial values back in place we get: 1+1 = 1
or 2 = 1
What is wrong with the proof above?
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5) Three people check into a hotel. They pay $30 to the manager and go
to their room. The manager suddenly remembers that the room rate is
$25 and gives $5 to the bellboy to return to the people. On the way
to the room the bellboy reasons that $5 would be difficult to share
among three people so he pockets $2 and gives $1 to each person.
Now each person paid $10 and got back $1. So they paid $9 each,
totalling $27. The bellboy has $2, totalling $29. Where is the
missing $1?
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6) You have 10 stacks of coins, each with 10 half-dollar coins in it.
One entire stack is counterfeit, with each counterfeit coin
weighing one gram more than it should. The weight of a normal half
dollar is known to be 5 grams. Using a standard scale, a person can
determine the counterfeit stack in just one weighing. How can this
be done?