Math Word Problems?

Question

1. Ten points are placed around a circle. A line segment is drawn between each pair of points. How many line segments are drawn?

2. A palidromic number is a whole number that remains unchanged when its digits are written in reverse order. Find a palidromic number that has four digits and is the fourth power of a natural number.

Answer 1

The first question is easy...

Each point (10 total) will connect to 9 other points, so that would be 10 x 9 line segments, except that counts them twice (a line from A to B is the same as a line from B to A). So just divide this product by 2 to get 45.

In general, with n points you would have n(n-1) / 2 line segments. For 10 points, there would be 45 line segments. This is often called the "handshaking formula" because if you had 10 people, and they shook hands with everyone else in the room there would be 45 handshakes.

Question two is harder, namely because it is impossible to find an answer.

Just doing trial and error, the only natural numbers that are four digits long when raised to the 4th power are:

6, 1296
7, 2401
8, 4096
9, 6561

None of them are palindromes. I suppose if you allow leading zeroes to be counted, you could say that 0^4 = 0000 which is a palindrome. But then you have to decide if 0 is a "natural number". In some definitions it is, others it is not.

Answer 2

1. To make a line segment we need 2 points n we have 10 points around the circle, so here we use combinations:
10 C 2
= 10! / 8! * 2!
= 10*9/2
= 45 line segments

2. First u need to check your Ques., becoz if u take the fourth power of natural numbers with the limitation that the resulting number should be a four digit number then you just need to check natural no's from 6 to 9, i hope u got the logic behind that. And when u calculate the fourth power of 6,7,8 and 9 you don't get any palidromic no. So, check your Ques. ok
And if u know, every successive power of number 11 gives a palidromic no.