# ATTN: spice and any MATH PEOPLE around =)

I need help with some math!!!

1. To transmit a positive integer less than 1000, the Networked Number Node offers two options:

Pay d to send each digit d.

Encode number into binary, then pay d to send each digit d.

What is the largest integer less than 1000 in which the cost of transmission is the same for both options?

2. Three players each have a red card, blue card and green card. The players will play a game that consists of three rounds. In each of the three rounds each player randomly turns over one of his/her cards without replacement. What is the probability that, at the end of the game, one card of each color was turned over in each of the three rounds? Express your answer as a common fraction.

3.

Matt will arrange four identical, dotless

dominoes (shaded 1 by 2 rectangles) on a 5 by

4 grid so that a path is formed from

the upper left-hand corner A to the lower righthand

corner B. In a path, consecutive dominoes

must touch at their sides and not just their

corners. No domino may be placed diagonally;

each domino covers exactly two of the unit

squares shown on the grid. How many distinct arrangements are possible?

4. A circular tabletop is divided into 4 sectorsby two diameters that are perpendicular to each other. Each sector is to be painted with 1 of 4 colors. How many distinct ways can the table be painted?

Full solutions and help would be appreciated here.