• 1000个人站成一个圈， 1号杀 2号， 3号杀 4号，轮到每个人时候都杀他下一个，一直循环到最后只有一个人为止，问最后剩几号？

• 1) In three separate trips, we will transfer the 3000 apples to our first stopping point. At the first stopping point, we want to have as close to 2000 apples as possible. This way, when we start moving again, we have as close to 1000 apples as possible in our truck.

• This leads us to solving: 3000-3*x=2000 => x~333.33 miles (round up to 334), where x is the distance in miles we travel to the first stopping point. Note that we multiply 'x' times 3 since we are taking the apples in three separate runs. After truckin' the 3000 apples, in three separate runs, 334 miles, we have 3000-3*334=1998 apples left and 666 miles left to go.

• 2. 抛一个 10个面的 dice，数字分别为 1-10。记下每次抛后的面值并做累加，一旦总和超过 100则停止。请问最终最有可能得到的总和值为多少？

• 101

• 1. mental arithmetics (no calculator, no paper and pen)

• 43-87=?

• 11%*182=?

• 38*42=? What is the percentage you are confident with your answer?

• 2. I roll a die, and I will give you an amount in pounds equal to the number on the die. For example, if I get 5, I will give you 5 pounds. What is the price you are willing to pay for this game? (a: 3.5)

• now say that when you roll the die, you are allowed to either take the money that you get with the roll, or roll a second time. But you have to take whatever it is of the second roll. what is the price you willing to pay to play? (a: 4.25)

• 3. 3 coins, what is the probability that I get at least two heads? If 4 coins, what is the probability that I get at least two heads? How confident you are with this answer? (a: 0.5, 11/16)

• 4. One normal ball has length 8-inch weighs 80kg, what is a 12-inch ball weigh? (a: 270kg)

• 5. If I drop a ball from 10 meters high, it will always rebound half the distance, e.g. the first time, it rebounds 5m high, then the second time 2.5m, etc. So how long does the ball travel after it finally stops? Confident? (a: 30m)

• 1. 12% of 47 • 2. a deck of card (no joker), if I turn the first two cards around, find the

probability that both cards will be ace • 3. flip four coins, get $1 for head and zero for tail, find the price you need to

pay to play this game • 4. How confident are you with the previous questions you have answered?

5. a) roll two dice, add the values, you and your component to pick a number represents the sum of two dice, which number will you pick? would you go first or second b) if the probability of getting 12 is 40% and the rest is a uniform distribution of 60%, which number would you pick now? 5. two player A, B are to play a game (7 rounds in total), the game terminates if any of the player wins 4 games. The winning probability of each player is a 1/2, find the probability that both players will be playing the 7th round.

• You are given a six sided die. What is the expected value of the difference between the two dice rolls?

• 35/18

• I am thinking about two positive integers: a and b. I can tell you a/b is belong to the close interval [0.48, 0.52], then give me all the possible values for b no matter what value a takes.

• 2,4,6,8...24,25,26,27,28...

• Expected value of a dice if you can reroll up to 3 times and take the highest number.

• 119/24

• - A car has a uniformly distributed value between 0 and 1000. If you bid less than this value, you get nothing but keep your bid. If you bid more than this value, you can sell the car for 1.5 times the value. What should you bid? - The surface of a 3x3 block is painted. The block is split into 27 cubes and one is dropped on the floor. What is the probability that no visible face is painted? If no visible face is painted, what is the probability that it is the centre cube?

• 1) 0 2) 2/27; 1/2

• 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.

• 2500 5/18 x=1.5, bid 0 x=2.5, bid 1000 17/06/2345

• How many digits is 99 to the 99th power.

• 197

• There are four coins. For each heads you get, you get $1. You can also re-flip one coin after the initial four flips. What is the maximum you would pay to play this game?

• 79/32

• How many tons does the ocean weigh?

• toss two dice. if the sum is 7, you win a dollar. if the sum is even, you lose a dollar. otherwise, roll again. what is the expected payoff?

• -0.5

• how much water is there in the ocean

• how many people are currently on the plane

• You are given a 100 sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the expected value of the game?

• 87

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