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if you have a 6 by 6 matrix where each element is either 1 or -1, how many unique matrices are there such that each row and each column multiplies to 1.

4 Answers

Q:(i) How many 7-digit numbers are in the form of abcdcba (symmetric about the digit in the middle)? (ii) What is the average of such numbers?

6 Answers

A seller is selling you a car whose value is uniformly distributed between 0 and 1000 but you don’t know the real value and you need to bid for the car. If your bid price is higher than the its real value, the deal will be done at your bid price and you can afterwards resell the car elsewhere for 1.5 times its real value. Otherwise, the deal will not be done. You can only bid once. What will be your optimal bid price?

5 Answers

Round 2: If you have balls weighting from 1, 2, ... 40g, and you have a fair balance, how many of their weights you have to know in advance such that you can measure all the rest?

5 Answers

Sum the odd integers between 1 and 100. Roll two die, what is the probability that the sum of the pips on the die are at least 9. There is a car auction. The price of the car is uniform [0,1000], you do not know the actual value of the car. If you bid higher than the value of the car you get it, if you bid lower than the value of the car you don't. If you know you can sell it on afterwards for x times its worth, what should you should you bid when: x=1.5 x=2.5 e.g. for x=1.5, you bid 100, the car is worth 80, you get it and sell it on for 120, which is a 20 profit. What is the next date that the day month and year share no common values. e.g. 13/11/2014 has four '1's so doesn't count.

3 Answers

At the bus stop 3/4 of commuters leave the bus and 7 new come in. This process repeats 3 times. What is the minimal number of people initially in the bus.

3 Answers

I have two cards that can only be red or black. I tell you that at least one of two is red. What's the probability that I hold two reds?

5 Answers

Today is 15/09/2011,what's the nearest day in the future that all the eight digits are unique?

3 Answers

what is the stock index in the Netherlands? Tell me some option trading strategies.

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Have a tricycle. Will travel on it for 1000 miles. Have two spare tyres with you (hence 5 in total). a) If you want each of them to be worn the same by the end of the journey, how much will each of the tyres travel on the ground. b) What is the minimum number of stops you have to make in order to achieve this.

3 Answers
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