The worlds first riddle!

But 4 is not congruent to 1 for any mod other than 3.

[size=7]225
11,111,111,100[/size]

prime modulo


Rough and dry
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niTin
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A Barber has a shop in a village, the shop has a board written on it "I shave those who don't shave themselves". Hmm... Will the barber shave himself???




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niTin----
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Mark:

CIRCLES Sweet!
* 3 5 *
7 1 8 2
* 4 6 *


225
11,111,111,100 Sweeter!


Yup! 11111111100

225 = 9 * 25
divisible by 9 means sum of digits is divisible by 9
divisible by 25 ending in 0 or 1 has to be 100.




Using only the numbers 16,18,20, 22,24,26,28,28,,32,36.

Can you ensure every row totals 100

_ _ _ _0 _ _ _ _
0 _ _ 0_0_ _ 0
_ _ 0_ _ 0 _ _
_ _ _ _ 0 _ _ _ _
_ _ 0 _ _ _ _ 0 _

There are supposed to be five lines of four. (Star)


Should anyone find that too easy (yes, I am talking to you Mark) chew on this:


Fill in the 4x4 square, in such a way that the sum of the numbers in each row (horizontally, vertically, and diagonally) is 264, even if you hold the square upside down. You are only allowed to use the digits 1, 6, 8, and 9, and each number may appear only once in the square

I take pity on you and give the first line - 25% correct.


18 99 86 61
* * * *
* * * *
* * * *

An Idea can change your life.....

As it goes...................................


A function
f:{0,1}* --> {0,1}*
is called one-way if the following two conditions hold:

1. easy to compute:
There exists a (deterministic) polynomial-time algorithm, A, so that on on input x algorithm A outputs f(x) (i.e., A(x) = f(x))

2. hard to invert:
For every probabilistic polynomial-time algorithm, A', every polynomial , and all sufficiently large n's


If Un denotes a random variable uniformly distributed over {0,1}n, the probability in the second condition is taken over all the possible values assigned to Un and all possible internal coin tosses of A' with uniform probability distribution. In addition to an input in the range of f the inverting algorithm is also given the desired length of the output in unary notation. The main reason for this convention is to rule out the possibility that a function is consider one-way merely because the inverting algorithm does not have enough time to print the output.

It is not known whether one-way functions exist. In fact, their existence would imply P≠NP, resolving the foremost unsolved question of computer science. However, it is not clear if P≠NP implies the existence of one-way functions. It is also not clear if the existence of one-way functions implies the existence of one-to-one one-way functions. However, it has been shown that P≠UP (a subclass of NP) implies the existence of one-to-one one-way functions; see UP for more. It can be proved, that weak one-way functions exist if and only if strong weak functions do. Thus, as far as the mere existence of one-way function goes, the notions of weak and strong one-way functions are equivalent.

The twin prime conjecture is a famous problem in number theory that involves prime numbers. It states:

There are an infinite number of primes p such that p + 2 is also prime.

Such a pair of prime numbers is called a twin prime. The conjecture has been researched by many number theorists. Mathematicians believe the conjecture to be true, based only on numerical evidence and heuristic reasoning involving the probabilistic distribution of primes.

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A palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns. The first few decimal palindromic primes (sequence A002385 in OEIS) are:

2, 3, 5, 7, 11, 101 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, …
It may be noticed that in the above list there are no 2- or 4-digit palindromic primes, except for 11. If one considers the divisibility test for 11, it can be deduced that any palindromic number with an even number of digits is divisible by 11.
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An Idea can change your life

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It is not known if there are infinitely many palindromic primes in base 10. The largest known palindromic prime is 10130022 + 3761673 ?- 1065008 + 1, which was found by Harvey Dubner on November 7, 2004 and announced on November 19, 2004.

Hi niTin good to see you back dude. However, I am obliged to point out that, before you set questions you must answer one (correctly). Should you wish to challenge this paradox check with Bertrand Russell.

"An Idea can change your life"

An application of an idea will change the life of others.

100 STAR


4X4 SQUARE
[size=7]18 99 86 61
66 81 98 19
91 16 69 88
89 68 11 96[/size]

I always try to follow you ppl but damn... i am too SLOW at working solutions. Ya, its a very famous Paradox. And the answer doesn't lie in the Set theory.....
Which set does the barber lies in....
>The ppl who shave themselves.
>or the ppl who don't shave themselves.

The Answer is not possible.
Genuine Paradox.


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---------------niTin
And ya an Idea can change your & others lives, provided you apply it.
BINGO.... Cheers

NiTin wrote
1. easy to compute:
There exists a (deterministic) polynomial-time algorithm, A, so that on on input x algorithm A outputs f(x) (i.e., A(x) = f(x))

crickey! I chose to play with the big kids here.

Mark:

16
18 24 36 22
28 20
26
32 28

That is AMAZING I have:

36
26 18 28 28
22 16
32
24 20

I never thought there could be more than one solution.

4X4 SQUARE
18 99 86 61
66 81 98 19
91 16 69 88
89 68 11 96

I would also accept:
18 99 86 61
81 66 19 98
69 88 91 16
96 11 68 89


niTin wrote, "i am too SLOW at working solutions"

That makes two of us



Dadpad wrote, "crickey! I chose to play with the big kids here."

Your bloody lucky mate, I don't even know how to play crickey! But judging from the ashes result, nor does anyone in OZ, except S.W.


Is an old hundred dollar bill better than a new one



Which is correct to say,
"The yolk of the egg are white," or
"The yolk of the egg is white"


There is an ancient device that allowed attacking armies to pass thru solid stonewalls. What is it



Game over:

A rich mathematician decided that he would give every man $45 and every woman $60. Only one ninth of the men and only one twelfth of the women collected their dues.

Can you tell me how much money the mathematician spent if there were 3552 people in total

No way man! No freekin way

[size=7]EGG
The yolk of the egg IS yellow.

ANCIENT DEVICE
teleporter

MATHEMATICIAN
So on average, each man collected $5 and each woman collected $5. Therefore, on average each of the 3552 people collected $5. He spent $17,760.[/size]

$100 or $1.00 hmm let me think.......

Egg yolks are yellow my friend. unless they eggs from a story by Dr Suess when they might just be green.

Ancient device: A portcullis?

There is no such thing as a rich mathematician. This this question gives 17,750 reasons why.

We have no further interest in crickey, thank- you- very- much. We are developing a world championship farnarkling team for the world farnarkling championships in March.

How can you lift an elephant with one hand?

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niTin
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An Idea can change your life.
....................
..............
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so..........I didnt know elephants had hands!
...........
see you learn something new every day.

Mark:
EGG
The yolk of the egg IS yellow.

ANCIENT DEVICE
teleporter

MATHEMATICIAN
So on average, each man collected $5 and each woman collected $5. Therefore, on average each of the 3552 people collected $5. He spent $17,760. ,


Dadpad:

$100 or $1.00 hmm let me think.......

Egg yolks are yellow my friend. unless they eggs from a story by Dr Suess when they might just be green.

Ancient device: A portcullis?
(Good enough, I have ?'Door')


There is no such thing as a rich mathematician. This question gives 17,750 reasons why.
(Sooooo close, 10 more mate)

If there are x men, then there are (3552 - x) women.

Thus one ninth of the men (= x / 9) received $45 and one twelve of the women (= (3552 - x) / 12) received $60.

So the total recevied is (45 * (x / 9)) + (60 * (3552 - x) / 12), the x cancels leaving 5 * 3552 = 17,760.



Dadpad wrote, "We are developing a world championship farnarkling team for the world farnarkling championships in March."

I don't think so…

"In a shock decision by the International Farnarkling Board, the Australian Farnarkling team have been disqualified from playing in the 2006 World Series for using a non-regulation Furby during practice. Spies sent from the Dominican Republic revealed that they had obtained the illegal Furby from a Zulu pict during Hogmanay in Abergavenny, and was thus two kilos under weight. This allowed the Australian team to avoid passing while during knip, as the Furby could safely be bounced along the ground at a rate not equal to the speed of mud."

Tiddlywinks anyone? :wink:


In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest.
When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.

How many people have guessed three fruits correctly
How many people have guessed four fruits correctly



There is a pole in a lake. Half the pole is in the mud, another third of it is covered by water, and eight feet is out of the water. What is total length of the pole in feet


Or any comparative measurement system (except for the Brits, ?'Rod, Pole and Perch)

Is it just me, or are the questions getting easier?
Except for the Elephants that is.

10 people guessed four fruits correctly, while 0 guessed three fruits because it would be impossible

[size=7]POLE
48 feet[/size]