Its been a busy two weeks. As we complete Dunnhumby and Absolutdata hunts, we are talking to few more analytics companies and are in the process of getting more analytics hunts.
Let me briefly put the solutions of Dunnhumby hunt.
Lets take for example The following question.
Rajesh is given a normal six sided cube and six colors - Red, Blue, Green, Yellow, Orange and Violet. He is supposed to paint each side of the cube with one color. How many 'different' cubes can Rajesh make? Note : Different means even if you rotate the cube and see, they don't appear like any other cube.
Let X be the number of different cubes and Y be the number of ways you can 'align' a given cube in space such that one face is pointed north, one is east, one is south, one is west and one is up, and one is down. Then the total number of possibilites is X*Y. Each of these possibilities looks different because if you could take a cube painted one way and align it a certain way to make it look the same as a differently painted cube aligned a certain way, then those would not really be different cubes. Also note that if you start with an aligned cube and paint it however you want, you will always arrive at one of those X*Y possibilities. How many ways can you align a given cube? You have six options for the north side, five for the east etc. So 6! How many ways can you align a given cube? Choose one face and point it north. Six options here. But the one pointing south is already fixed. Now there are four options for pointing east. There are no further options for alignment, so the total number of ways you can align the cube is 6*4 l Y is defined as the number of ways you can align the cube so Y = 6*4; Therefore 6! = X*6*4 so X = 30;
'500!' - how many trailing zeros? Very simple and I am not going to solve this.
Vishnu, Rajesh and Hari live in three corners of the city as shown in the figure. There is only one road that connects each of their houses as shown in the image. Their birthdays fall on the same day and they always celebrate it together. On their 21st birthday each of Vishnu, Rajesh and Hari plan to suprise each other. They all start moving randomly from their residence to one of their friends residence. What is the probability that they don't meet each other? (If the answer is 1/2, your answer format should be '0.50'
Lets call them A,B,C. There are two cases when they will not collide - all move clockwise or anticlockwise.They will collide if two ants move towards each other and the third ant can move in any of the two given directions. And there are three such pairs. So 3*2 such cases. So probability of them not colliding is 2/(2+6) = 0.25
You buy a new battery for your clock. The clock is set right at 10AM on Monday morning. It looses 0.5% on the correct time in the first week but gains 0.25% on the true time during the second week. The time show on Monday after two weeks will be ? (Answer format is HH:MM:SS)
Week 1: The clock loses (1/2)% of the actual time
To LOSE time is to OVERCOUNT the number of hours. Let's say that we must leave a party at 2pm. If the clock overcounts the number of hours and reads 2pm when the time is really 1pm, we will leave 1 hour EARLIER than is necessary, with the result that we LOSE one hour of party time. Here, the number of hours OVERCOUNTED = (1/2)/100 * 168 = 84/100 = .84 hours. Thus, at the end of week 1, the clock is AHEAD .84 hours.
Week 2: The clock gains (1/4)% of the actual time
To GAIN time is to UNDERCOUNT the number of hours. Let's say we that we must leave a party at 2pm. If the clock undercounts the number of hours and reads 1pm when the time is really 2pm, we will leave the party 1 hour LATER than is necessary, with the result that we GAIN one hour of party time. Here, the number of hours UNDERCOUNTED = (1/4)/100 * 168 = 42/100 = .42 hours. In other words, the clock MOVES BACK .42 hours.
Net change for the two weeks = .84 - .42 = .42 hours.
Since 1 hour = 60 minutes, we get:
(1 hour)/(60 minutes) = (.42 hours)/(x minutes)
x = .42(60) = 25.2 minutes = 25 minutes, 12 seconds.
Since the clock is AHEAD by 25 minutes, 12 seconds, the time shown = 10:25:12.
The ages of six friends are 31, 52, 58, 63, 66 and 72. The sample variance is ? (round off to two decimal places)
Fairly simple - http://www.ajdesigner.com/phpstatistics/variance_sample.php
The two data analysis questions can be solved both in SAS and excel. Once you relate with the question, it is fairly simple!
The case study was a trick question. Once you identify what data to use, it is a very simple question.
