Monthly Archives: July 2005

How Many unique ways are there to form this set A?

N is the set of all Natural Numbers from 1 till 500.
N is the set of all Natural Numbers from 1 till 500.

From this set we have form a set A such that

1. Any pair of 2 elements of A are relatively prime that is if x,y element of A then HCF(x,y)=1

2. A has got Maximum possible number of Elements

Now the question is

How many unique ways are there to form this set A such that Both the rules [1,2] are satisfied.

Solution:

5760

Explanation:

These are the following figures: 250*68*33*19*11*8*5*3
where 250 is for multiples of 2 (only one can be picked),
68 is for multiples of 3 less multiples of 6 (only one to pick),
33 for multiples of 5,
19 for 7,
11 for 11,
8 for 13,
5 for 17 and 3 for 19
replace 2 with powers of 2 of less than 500, so u have 8 options, simlarly 5 for 3 so the ans is
8*5*3*3*2*2*2*2 for 2,3,5,7,11,13,17 and 19 respectively

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4000+2000 = 0

Can you solve the below problem which is mathematically justified?

A methematician was bought to the court on charges of money laundering. The plaintiff claimed that the accused initially borrowes 2000 from them then further borrowed 4000. Thus the accused has to pay a total of 6000.

The accused did not have any defense and was in dire straits. Being a good mathematician and at his wits end, he told the judge that he owes the plaitiff nothing as 2000+4000 adds up to 0.

He offered to prove it mathematically to the judge and plaitiff and does so to their astonishment.

Can you too?

Solution is below.

let a = 4000, b = 2000 and c = 6000

a + b = c

Multiply both sides by a + b

(a + b) (a + b) = c (a + b)

a*a + ab + ba + b*b = ca + cb

a*a + ab - ca = cb - b*b - ba

a(a + b - c) = -b(b + a - c)

a(a + b - c) = -b(a + b - c)

now (a + b - c) is cancelled out giving

so a = - b

a + b = 0
or
4000 + 2000 = 0


Now that you have seen the solution, can you point out the fallacy in the above logic? The solution is again below:

By the Cancelation Property of Equality


xz = yz => x = y if an only if z not equals zero

In this case:

(a + b – c) cannot be cancelled as we have earlier said that

a + b = c => (a+b - c) = 0

What say you?

The Death of Toleralism


For centuries the Netherlands has been considered the world’s most tolerant and liberal nation. This attitude is a byproduct of a disciplined civic society, confident enough to provide space for those with different ideas. It produced the country in which Descartes found refuge, a center of freedom of thought and of a free press in Europe. That Netherlands no longer exists.

The murder of Theo van Gogh last year and the assassination of Pim Fortuyn in 2002 marked the end of the Holland of Erasmus and Spinoza. Their killings showed the cumulative effect of two forces that have shaken the foundations of Dutch civic society over the last 40 years: the cultural and sexual revolution of the 1960s and 1970s and the influx of Muslim workers during those years of prosperity.

Perhaps no country was affected as profoundly by the radicalism of the times as the Netherlands. In less than 15 years, most forms of traditional authority and hierarchy, the counterbalancing forces that made Dutch tolerance possible, were undermined. Hence today’s image of Dutch tolerance: marijuana served at coffee shops, police officers with hair as long as the Grateful Dead, full nudity on public television and, for those who prefer not to work, a government package of benefits that makes a toil-free life entirely feasible.

The second, simultaneous, change in Dutch life was the recruitment of young men from the Rif Mountains of Morocco, most illiterate and many with only a rudimentary grasp of spoken Dutch, to work in Holland’s rapidly expanding industries. When they arrived, they were faced with a highly educated but apparently decadent society in the grip of a cultural revolution. Many were astonished: Was this country some sort of freak show?

No, it certainly wasn’t. Under the effusive “anything goes” exterior, the majority of Dutch people held on to their disciplined Calvinist values. To the immigrants, however, this core was all but invisible.

During the 1980s and 90s, the demand for unskilled work declined. The “guest workers” were no longer needed in such numbers, but they were also not required to return to Morocco. Instead they were given extensive social benefits and their families were allowed to come from Morocco to join them. It was the birth of the ethnic-religious ghettos that surround our affluent cities and towns.

And thus the delicate mechanism of Holland’s traditional tolerant society gradually lost its balance. The news media, politicians and artists gnawed away at the traditional values of Calvinistic civic society, while in the bleak Muslim suburbs resentment grew among the Moroccans’ Dutch-born children, who found the promise of an affluent life unfulfillable.

Meanwhile, the news media and politicians maintained an unofficial ban on any discussion of the problems of immigration: after all, in progressive Holland only socioeconomic problems were admissible. It was simply not acceptable to discuss problems relating to religion and culture.

This mix of cultural confusion, religious misunderstanding and political correctness provided the stage on which Pim Fortuyn performed. In the international press, Fortuyn was often described as a right-wing radical, a label he loathed. He was a liberal with respect to personal freedom and a conservative with respect to social norms and values – that is, he was a classic tolerant Dutchman.

Proud to be gay, he protested against the religiously-based homophobia openly espoused in the Muslim ghettos. Yet he also emphasized the need for integrating Muslims into larger society and tolerance for their faith. His political incorrectness shocked the establishment, but many among the traditional citizenry recognized Fortuyn as a kindred spirit. This unconventional gay politician spoke up for the conventional middle-class heterosexual. At the time he was killed by an animal-rights advocate in 2002, he was the front-runner to become prime minister.

The films of Theo van Gogh, artiste provocateur nonpareil, were meant to shock; his newspaper columns (of which I was the target more than once) were exercises in outlandish mudslinging – though never lacking in humor and style. In recent years, he had focused increasingly on the problems with immigration and Muslim intolerance.

The radicalized children of disappointed Islamic immigrants were unable to appreciate the humorous side of the Van Gogh phenomenon.

Many of these young men have found an expression for their growing sense of frustration, alienation and anger in orthodox Islam. They have no use for Holland’s tolerance of alternative lifestyles, or for its professional blasphemers. Last Nov. 2 a young Islamic fundamentalist, born in Amsterdam to Moroccan parents, shot Van Gogh in the street and then tried to cut off his head. In a final statement at his trial last week, the murderer declared that he had killed Van Gogh for insulting the Prophet.

The trial lasted only two days, but the fallout will be with us for many years. Much of the electorate no longer feels any loyalty to the existing political parties. Many want to preserve the Dutch welfare state, but it’s unclear how to maintain it in an aging nation that is absorbing immigrants. Without a radical change in direction, Dutch tolerance may become its own victim. The first step is enacting laws to curb immigration from Islamic countries. We must also consider ways to prevent arranged marriages between Muslims living here and people from the Rif (more than half of Dutch Moroccans marry a traditional partner from their parents’ home village).

In the longer term, we must somehow stimulate young Muslims to identify with the Calvinist values of the majority. The radicalization among small groups of young Muslims, a threat that cannot be fought within Holland’s borders alone, is a time bomb.

Perhaps what this country needs most of all is another unconventional, outspoken gay politician.

(Leon de Winter is a novelist and political columnist for Elsevier magazine.)