Phone interview: 1. A n by n by n cube, painted all outside surfaces. Then cut it into 1 by 1 by 1 cubes. These cubes have faces that are painted and some faces not painted. The ratio between painted faces and number of cubes is 2:3. What is n? 2. A regular dice. (six faces, with 1,2,...,6 dots on each face) Now one dot is randomly selected and removed. Then we toss the dice. What's the prob that a face with odd No. of dots facing up? 3. You have some coins in pocket (pennies, nickels, dimes, quarters). The average value is 20 cents. If you add 1 more quarter to the sum, the average became 21 cents. How many dimes you have in pocket? (I asked if I can have none of any kind and he said yes) On-site interview: 1. A tug boat is lugging a cable of 8km long which has signal receivers on it. The receivers are evenly distributed with a distance of 12.5m between each of em. The boat keeps moving forward and every 50 meters, it fires a signal wave downwards the seabed. The signal is then bounced back and received by receivers on the cable. The middle point between the position where the signal was fired and the receiver picking up this very signal is called TMP. Therefore, one fired signal has 1 TMP per receiver but there're so many receivers on the cable. So one fired signal can have many TMP's. But one TMP may be corresponded to many signal/receiver pair as the boat is moving and it keeps firing. Question is how many fold (signal/receiver pair) for one TMP? 2. A 4x3 table. Ignore four corner cells, leaving 2+4+2=8 cells in total. Any two cells that have a side or a corner sharing are called "neighbors". Find a way to fill in numbers 1-8 into these 8 cells that no neighbor cells have consecutive numbers in them.
