Interesting Mathematical Aphorisms

Daniel Takacs

If you want to see some other interesting Trivia check this out MORE TRIVIA

This page was last updated on Nov. 10, 1999. Here is a link to all the solutions that I have: solutions more solutions solutions2. Also, if you know of any other interesting problems please send e-mail them to me.

CAN THIS BE TRUE?

WHERE IS THE DOLLAR?

There were three men who went to a hotel. They paid $30 for a hotel room. Approximately an hour later the manager saw their receipt for the room and told the bus boy to bring up $5, because rooms were on sale for $25. While the bus boy was going upstairs he thought "Why would I give this $5 back to the people. They do not even know they overpaid for their room." So the bus boy took $2 and only gave the men $3 back. Now every person paid $9 each for their room and the bus boy took $2. This means that the men paid 9*3 + 2 = $29 for their room.
Where is the $1?

IS 1 = -1?

1 = sqrt ( 1 )
1 = sqrt ( (-1)^2 )
1 = ( sqrt ( -1 ) )^2
1 = ( i )^2
1 = -1

SURE 1 = -1 AND 1 = 2 BUT DID YOU KNOW THAT NUMBER -.5 DOES NOT EXIST?

x = -.5
2x = -1
2x + 1 = 0
(x^2) + 2x + 1 = x^2
(x + 1)(x + 1) = x^2
(x + 1)^2 = x^2
x + 1 = x
1 = 0
Since we KNOW 1 is not equal to 0, we have proven that the number -.5 doesn't exist. :-)

A TRIANGLE WITH TWO SEPARATE ANGLES EQUAL TO 90 DEGREES!

Take a look at the following triangle and read the 'proof' bellow.

Construct triangle ABC. Let E be the midpoint of AC,
Let angle(ABF) = angle(FBC)
Triangle(ADE) = Triangle(CDE)
Triangle(GBD) = Triangle(HBD)
since BD is common, BG = BH and
angle(GBD) = angle(DBH)
Therefore GD = DH.
Now we have triangle DAG = CHD
Now angle(EAD) = angle(ECD) and
angle(GAD) = angle(DCH) therefore
angle(BAC) = angle(ACB) = 90

FIND DIGITS a, b, c AND d!

Find the digits a, b, c and d where abcd * 9 = dcba. Note you cannot make all of the digits a b c and d 0s.

FIND A NUMBER SUCH THAT ...

Find a positive integer such that when divided by 3 the remainder is 1, divided by 5 the remainder is 2 and when divided by 7 the remainder is 3.

PLEASE DO NOT BLOW UP THE TOWN!

There is a town with 3 houses and 3 companies. Company 1 sells gas, company 2 sells oil and the third company sells phone service. Your task is to connect these companies with the houses such that cables do not cross. If there are cables crossing there is an EXPLOSION! NO Cables through Houses!

House1 House2 House3

Compa1 Compa2 Compa3

2 = 1!

x=y
x^2=xy
x^2-y^2=xy=y^2
(x+y)(x-y)=y(x-y)
x+y=y
x+y=y
2y=y
2=1

FIND MORE NUMBERS IF THERE ARE ANY SUCH THAT

Try to find a Cyclic # such that as 0 or 142857. If this number is * by 1, 2, 3, 4, 5, 6 you will get the same number, only in a different order such as 2 * 142857 = 285714. Your job is to find more of these numbers.

Now if you thought this was easy, try to figure out a number that you can multiply by numbers from 1 to 200 and the number is cyclic.

HOW HIGH UP IS THE LADDER?

A cube 6' on a side is against a vertical wall on a level floor. A 30' ladder stands on this floor, against the wall, at an angle so that it just-touches the corner of the cube. How high up the wall is the point of contact of the top of the ladder?

COMPARISONS OF WEIGHTS!

You have 12 balls. All of them are of same weight but one. You have a scale with two pans. You have to find the odd ball in three weightings....

PRIME INFLUENCE:

Write any three digit number twice in the same order to make a six digit number, for example: 137137, divide this number by 13: 137137 % {divided by } 13 = 10549,
now divide 1059 by 11: 10549 % 11 = 959
now divide 959 by 7: 959 % 7 = 137
hence any three digit number taken twice and divided by 13, 11 and 7 gives the three digit number itself!

Now the problem is to find out why this works this way?

FIND THREE NUMBERS X Y Z SUCH THAT:

(x^2-1)^2 + (y^2-1)^2 = (z^2-1)^2

WHAT IS THE WIDTH OF THE ALLEY

Two ladders 30ft and 20 ft stand in an alley way such that each ladder goes from the base of one wall to the opposite wall. The height from the ground at the point where the ladders cross is exactly 10 ft.

1 = 2 AGAIN!!!

a=b a-2a+b=b-2a+b -a+b=-2a+2b (-a+b) / (-a + b ) = 2(-a+b) / ( -a + b) 1=2

ANOTHER LADDER!

Fire Department regulations state that a ladder must be positioned from a wall at a distance equal to 30% of the length of the ladder. If the wall is 5 feet tall, what distance from the wall will the ladder be placed.

COMPLETE THE WORDS:

INSTRUCTIONS: Each equation below contains the first
letters of the words that make a correct statement.
Find the missing words.

For example, 26 = L of the A
would become 26 = Letters of the Alphabet.

a) 26 = L of the A
b) 2001 = A S O
c) 12 = S of the Z
d) 54 = C in a D (with the Js)
e) 9 = P in the SS
f) 88 = PK
g) 13 = S on the AF
h) 18 = H on a GC
i) 200 = D for PG in M
j) 32 = DF at which WF
k) 90 = D in RA
l) 8 = S on a SS
m) 3 = BM (SHTR)
n) 4 = Q in a G
o) 24 = H in a D
p) 1 = W on a U
q) 5 = D in a AC
r) 57 = HV
s) 11 = P on a FT
t) 1000 = W that a P is W
u) 29 = D in F in a LY
v) 64 = S on a C
w) 40 = D and N of the GF
x) 13 = F of the N T is T
y) 8 = B in a B
z) 4 = B in a N
1) 6502 = P of the A 2E
2) 1415 = F F D of P
3) 1492 = C D of N W
4) 632 = S of H C
5) 2 = # it T to T

N MEN

A group of " n " men meets armed and disposed in a circle. To the fire sign, each one throws in one of its neighbors, the left or the right, in a circle. All the shots are simultaneous, well-aimed and humans.
1) to determine the numbers minimum and maximum of survivors after the fire sign.
2)For a given value of " k ", 0 <= k " <= n ", in what conditions the k survivors' occurrence is possible?
3)Repetir the previous item supposing that the objective of each shooter can be remaining anyone of the n-1.

TOUCHING CIRCLES

Consider, you have a large circle with 3 smaller circles inside it of varying lengths. Theses smaller circles are exactly touching the the edge of the larger circles and each other. they have distances of D1, D2, D3, accordingly. What is the formula for the area of the larger circle???

MOST POWERFUL DIGIT

If you had to choose the most powerful digit from the set of number from ( 0 - 9 ) which one would it be>

SOME REALLY AWESOME LATERAL THINKING EXERCISES!

Think of the solution...before u look immediately at the answers.

-1 There is a man that lives on the top floor of a very tall
building. Everyday he gets the elevator down to the ground floor to
leave the building to go to work. Upon returning from work though,
he can only travel half way up in the lift and has to walk the rest
of the way unless it's raining!
WHY? This is probably the best known and most celebrated of all
lateral thinking puzzles. It is a true classic. Although there are
many possible solutions which fit the initial conditions, only the
canonical answer is truly satisfying.

-2 A man and his son are in a car accident. The father dies on the
scene, but the child is rushed to the hospital. When he arrives the
surgeon says "I can't operate on this boy, he is my son!"
How can this be?

--3 A man is wearing black. Black shoes, socks, trousers, jumper,
gloves and balaclava. He is walking down a black street with all the
street lamps off. A black car is coming towards him with its light
off too but some how manages to stop in time.
How did the driver see the man?

---4 Title : The Elder Twin
One day Kerry celebrated her birthday. Two days later her older twin
brother, Terry, celebrated his birthday. Why?

---5 Title : Manhole Covers
Why is it better to have round manhole covers than square ones?
This is logical rather than lateral, but it is a good puzzle which can
be solved by lateral thinking techniques. It is supposedly used by
a very well-known software company as an interview question for
prospective employees.

---6 Title : The Deadly Party
A man went to a party and drank some of the punch. He then left
early. Everyone else at the party who drank the punch subsequently
died of poisoning. Why did the man not die?

---7 Title : Heaven
A man died and went to Heaven. There were thousands of other people
there. They were all naked and all looked as they did at the age of
21. He looked around to see if there was anyone he recognized. He
saw a couple and he knew immediately that they were Adam and Eve.
How did he know?

---8 Title : Trouble with Sons
A woman had two sons who were born on the same hour of the same day of
the same year. But they were not twins. How could this be so?

--- 9 Title : The Man in the Bar
A man walks into a bar and asks the barman for a glass of water. The
barman pulls out a gun and points it at the man. The man says
'Thank you' and walks out.
This puzzle has claims to be the best of the genre. It is simple in
its statement, absolutely baffling and yet with a completely
satisfying solution. Most people struggle very hard to solve this one
yet they like the answer when they hear it or have the
satisfaction of figuring it out.

A HUNDRED DOORS!

Suppose you have 100 doors lined up in a row. initially all of them are closed:
  Door1-Closed, Door2-Closed, Door3-Closed,.... Now suppose you walk down the chain of doors 100 times doing the following:
  If this is your first time you walk down you change every door,
  If this is the second time you walk down you change every second door
  If this is the third time you walk down you change every third door.
  ......
  If this is the hundredth time you walk down you change the hundred door.

change = if door is open then close it, or if the door is closed you open it

Now which doors will you have open after you walk down 100 times.

HOW MUCH DOES THE CORK COST?

You have a bottle and a cork, which both add up to $1.10. The bottle is a dollar more than the cork. How much is the cork?

CONTRIBUTIONS

I would like to thank all the people who have contributed to this page:

Nikolai Petrov
Chris Takacs
Mattias Andersson
John Jacobs
Also check out this page for more math stuff
MAth