Find the greatest product of five consecutive digits in the 1000-digit number.
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10001st prime number?
I am a total LaTeX newbie though, so I often struggle a bit with… getting it right. Trying it out by previewing WordPress posts is sloooow, so I decided to create myself a simple test-rig. A simple web page with a form and a button.
Let me know if you like it: tools.geekality.net/wp-latex 8)
The sum of the squares of the first ten natural numbers is,
The square of the sum of the first ten natural numbers is,
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 — 385 = 3640.
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
The other day I started reading a book called Wild at Heart. So far it has been a great book and fun to read. Certain things has already started to make a bit more sense than they did before.
Two of the many very interesting paragraphs from it:
There are three desires I find written so deeply into my heart I know now I can no longer disregard them without losing my soul. They are core to who and what I am and yearn to be. I gaze into boyhood, I search the pages of literature, I listen carefully to many, many men, and I am convinced these desires are universal, a clue into masculinity itself. They may be misplaced, forgotten, or misdirected, but in the heart of every man is a desperate desire for a battle to fight, an adventure to live, and a beauty to rescue. I want o you think of the films men love, the things they do with their free time, and especially the aspirations of little boys and see if I am not right on this.
There are also three desires that I have found essential to a woman’s heart, which are not entirely different from a man’s and yet they remain distinctly feminine. Not every woman wants a battle to fight, but every woman years to fought for. Listen to the longing of a woman’s heart: She wants to be more than noticed—she wants to be wanted. … Every woman also wants an adventure to share. … So many men make the mistake of thinking that the woman is the adventure. But that is where the relationship immediately goes downhill. A woman doesn’t want to be the adventure; she wants to be caught up into something greater than herself. … And finally, every woman wants to have a beauty to unveil. Not to conjure, but to unveil. Most women feel the pressure to be beautiful from very young, but that is not what I speak of. There is also a deep desire to simply and truly be the beauty, and be delighted in.
OK, actually that last one is three paragraphs in the book. But tried to get the similar three points that was mentioned for men (And for men they are each elaborated in three sub chapters).
Aaaanyways, very interesting book. You should definitely read it, especially if you are a guy. Could be interesting if you are a woman too of course, but I can only speak for myself, who is a guy. For women there is actually a similar book called Captivating, which I have heard is very good as well. I haven’t read it yet though… but I will 😉
Highly recommend them! Get them from Amazon, they are not even expensive 😀
What do you think about this matter? Did it sound about right? What is in the innermost parts of your heart?
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?
The fourth problem was a bit tricky, but at the same time a bit funny.
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91*99.
Find the largest palindrome made from the product of two 3-digit numbers.