1. A helium-filled balloon is tied to the floor of a car that makes a sharp right turn. Does the balloon tilt while the turn is made? If so, which way? The windows are closed so there is no connection with the outside air. (I’ve tested this)

2. A person in a boat in his own [...]

Tags:

Physics
If the sum of the divisors of integer n is equal to 2*n, we call the number perfect. For example, the divisors of 28 are 1, 2, 4, 7, 14, and 28. 1+2+4+7+14+28 = 56 = 28*2.

Similarly, if the sum of the divisors exceeds twice the number, we call the number abundant. For example, 12 [...]

N = R* x ƒp x ne x ƒℓ x fi x ƒc x L

What does this equation mean?

If it is of any help, a rigorous estimate using the equation was implemented in 2001. It produced an estimated answer of… “hundreds of thousands”!

Tags:

Tom
Undulating numbers are of the form: ababababab… For example, the

following are undulating numbers: 1717171, 282828, etc.

1. What is the next undulating square number after 121 (11^2)

2. What is the next undulating cube numbers after 343 (7^3)

Tags:

Maths
How many 0’s are there in the numbers 1 to 1,000,000,000,000?

I refrain from the use of the word billion as our American cousins have difficulty in comprehending what a billion actually is (10^12, not 10^9)…. Flaming gratefully accepted at the usual address….

Tags:

Maths
How will create a Rand7() function using Rand5() function ?

RandX() function will return a random numbers between 0 to (x-1)

You have a meeting scheduled with the Devil. It’s on a Sunday, when you would normally be at church, but hey-ho – business before pleasure and all that. He wants revenge for having been foiled in the past…..

He proposes the following game:

Each of you will take turns placing a plate on a clean table. All [...]

Tags:

Tom
Give the formula for the coordinates of the intersecting rectangles formed by two separate rectangles in 2D space ?

The devil comes to you with a new offer. This time, you will walk up to a table with 864 gold coins on it. 216 of these coins will be ‘heads up’ and the rest ‘tails up’. Your task is simple, make two piles out of the coins with each pile containing the same number [...]

Here’s another: I believe that 2^(2*3^(n-1)) = 1 (mod 3^n), n > 0 where the power 2*3^(n-1) is the smallest possible and is the same as the Euler totient. Prove or disprove it. A single counterexample will suffice for the false proof.