## Power sum

If x = ( -1 ± i√3)/2 find the value of x^1999 + x^2000, where i = √(-1)

Archive for March, 2011

Posted by Chris under MathsChallenge (28 Responds)

If x = ( -1 ± i√3)/2 find the value of x^1999 + x^2000, where i = √(-1)

If H is the infinite set of all the positive integers having, at most, prime factors 2, 3 and 5. Show that the sum of the reciprocals of the elements of H = 15/4.

For clarity,the first few elements of H are: 1,2,3,4,5,6,8,9,10,12,…

Posted by Chris under Logic (79 Responds)

A camel has to transport as many as possible of an available 3000 bananas. For every complete mile it walks, it must consume 1 banana (regardless of its load). It can only carry up to 1000 bananas at a time. What is the maximum number of bananas it can transport to a place a 1000 [...]

Posted by Chris under Logic (26 Responds)

Three doctors and three patients are traveling together through a jungle when they come to a river. All the patients have a unique kind of fever which will infect the doctors if at any time there are more patients than doctors (suspend your disbelief). The patients can only survive without a doctor for two minutes. It takes [...]

Posted by DP under Tom (9 Responds)

This time we have only a single {fair} die and roll it exactly 5 times. What is the probability that you will roll exactly:

a) [2] 3’s?

b) [4] 6’s?

c) [0] 1’s?

There are four different positive integers that sum to less than 18. To determine those numbers you need to know their product and the smallest number. What are the numbers?

Posted by Chris under MathsChallenge (33 Responds)

Five points are arranged in space so that no more than three at a time can have a single plane surface pass through them. Each group of three points has an infinite plane pass through them. What is the maximum number of lines at which these planes may intersect?

Posted by Chris under Logic (9 Responds)

Mr. Tito collecting data for the census came across a house with three sisters; Ina, Meena, and Dika. There were no straight answers when he enquired about their ages. This is what he was told:

Ina said “all of us are over 24 years of age. Dika is the youngest and I am the eldest”.

“The difference between Dika’s age and [...]

There are 3 such single-digit numbers that when taken to a power other than 1, you can add the resulting digits and arrive at the original number.

7 ^ 4 = 2401; 2 + 4 + 0 + 1 = 7

8 ^ 3 = 512; 5 +1 + 2 = 8

9 ^ 2 = 81; 8 [...]

Posted by DP under Tom (30 Responds)

Billy and Tommy are in the soccer finals (football if you prefer, but it gets confusing here in the States). They are up against their biggest rival, and need this win.

There are 12 players on their team, and only 9 from each team are allowed on the field at one time.

Their team decides to play [...]