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Survey Of Mathematics Final Exam
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Survey Of Mathematics Final Exam 2025-2026Art Gallery Problem - Answer For any weird of random shape, you can always break it
up into triangles and determine the minimal number of vertices for which everything in
the room can be observed. EX. an Art Gallery containing priceless paintings. You want
to know where in the floor plan you should locate guards so that the entire floor plan is
in the line of sight of the guards.
Color the vertices (a, b, and c)
a=4
b=4
c=3
floor of v/3
11/3 floored = 3
Chap. 1
Story #1 - Answer 'That's a Meanie Genie'
Girl is given 9 stones from a genie, and has to find the heaviest stone, for inside is a
precious gem. She is given 2 scales, and she can use each one only once.
She finds the heaviest stone by separating the stones into 3 piles of 3.
First she weighs two of the piles, and if the piles weigh the same, the heaviest stone is in
the pile she didn't weigh. If one pile weighs more than the other, the precious gem is in
that pile.
When the has found the pile which the precious gem is in she takes two of the stones
from that pile and weighs them against each other.
The same thing happens, if the stones weigh the same, the heaviest stone is the one that
,was not weighed. If one stone weighs more than the other, that is the stone with the
precious gem.
Chap. 1
Story #2 - Answer ''Damsel in Distress''
A knight wanting to get across a moat has only two planks of wood, each 19 feet across.
Alas, the moat is 20 feet across, so they don't reach.
He gets across by laying one of the beams diagonal across one of the corners, then lays
the end of the 2nd plank on the middle of the diagonal one till it reaches the other side's
corner.
Chap. 1
Story #3 - Answer 'The Fountain of Knowledge'
Trey wants to have just 8 ounces of juice. All he has is a glass that holds 6 ounces and
another that holds 10 ounces. How does he do it?
He fills the 10-ounce glass full and pours into the 6-ounce glass until it is full, leaving 4
ounces in the 10-ounce glass.
He throws away what was in the 6 ounce glass, and then pours the 4 ounces that were in
the 10 ounce glass into the 6 ounce glass.
He fills back the 10 ounce glass, and fills into the 6 ounce glass till its full. Since, there
were 4 ounces of juice in the 6 ounce glass, once he pours some into it that means he
poured 2 more ounces of juice into the 6 ounce glass.
That means that there is 8 ounces left in the 10 ounce which is what needed.
Chap. 1
Story #5 - Answer ''Dodgeball ''
2 boxes. One is 6 boxes down and 6 boxes across.
The other is just 6 boxes lined up in a row.
Player One is in charge of the first box and Player Two is in charge of the second box.
, Player One starts a row across by writing X's and O's.
Player Two writes one X or O in the first box of his row.
The second player is trying to avoid having his one row match any of Player One's rows.
You want to be PLAYER TWO. As all that you have to do in order to win is write the
opposite of the first letter in Player One's first row, then opposite of the second letter in
Player One's second row, etc.
Chap. 1
Story #7 - Answer ''Let's make a deal''
3 doors. Behind two of the doors are donkeys, while behind one of them is your dream
car. You select one door, then the game host reveals to you one of the two doors you did
not pick to show you there is a donkey behind it. Now, he provides you the chance to
switch from the first door you have chosen to the last one that wasn't opened. It is
always better to switch, because if you switch then you will have a 2/3'rds chance of
winning.
Pigeonhole Principle - Answer ''If there are more items than options for the items, then
at least 2 items will share an option''
Fibonacci Numbers are. - Answer A sequence of numbers that are created by starting
with two 1's, then adding the previous two numbers.
ex. 1 1 2 3 5 8 13 21 34.
Fibonacci numbers appear in nature - Answer Flower, Pineapples, Pinecones. (spirals)
Where does the Golden Ration come from? - Answer It comes from the quotients of
Fibonacci numbers. if you divide the quotients they approach the Golden Ratio.
(quotient : the result of a division)
How do you write natural numbers as the sum of non-consecutive Fibonacci numbers? -
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