Number Sense Questions!!

[16422]

I've got a couple questions:


First, is there a faster way to do the following problem besides converting all numbers to base 10?

111(base2) + 222(base3) + 333(base 4) = ____________________(base 10)


Second:

If X+Y= 1/3 and XY= 3 then X^3+Y^3 = _______________

I have been doing ((X+Y)^2 - 2XY)(X+Y) - (X+Y)(XY)..


Third:

How many ways can Huey, Dewey, and Louie sit in a row of four chairs?

The answer is 24, so is it just 4! ?


Fourth:

1(1!) + 2(2!) + 3(3!) + ... + 6(6!) = _____________


Fifth:

Sum of the squares of Fibonnaci numbers?
1^2 + 7^2 + 8^2 + 15^2 + 23^2 + 38^2 + 61^2 = ______________

Sum of the squares of triangular numbers?
1^2 + 3^2 + 6^2 + 10^2 + 15^2 + 21^2 = ______________


Sixth:

Product of coefficients?
The product of the coefficients of the binomial expansion of (x+2y)^3 is ___________


~Thanks :)

[101dalmatians]

[101dalmatians]

[101dalmatians]

[101dalmatians]

[101dalmatians]

[101dalmatians]

[101dalmatians]

[nsguy1350]

[nsguy1350]

[nsguy1350]

[101dalmatians]

[101dalmatians]

[101dalmatians]