Can't We Just Flip A Coin?

Albert picked 37. There are more numbers from 37-100 than 1-37; Bradly will have a larger chance of being closer to the number if he picks a number on the side of 37-100. However, if he randomly picks, he will be at an advantage because the distance from 37 to n could be equal to his number to n. He solves this problem by picking the next larger number, 38.

My class at school was doing a debate in English and to see who would go first the teacher would pick a number between 1 and 10 and the closest person could say if they wanted to go first or second. So I thought, what would maximize my chances. For this problem it's 1 to 100, so it's still basically the same concept. Since Albert picked 37 the number that would maximize your chances of winning would be the number that gives you the highest chance, because there are more possible outcomes after 37 you would choose 38 so that the only way that you could lose is if Cathy picked a number that is 37 or lower which is a 37 percent chance of losing. On the other hand, if Albert choose 50, you could go either way because of the amount of outcomes of each side of 50 which is the same.

The number that would be chosen by the two players and the number Cathy has in her mind is between $0$ to $100$ (inclusive). Now, Albert guesses $37$ . Now, we see that the range from $0$ to $37$ is smaller than the range $37-100$ . So, the probability that the number in Cathy's mind is in $37-100$ range is greater than the number being in $0-37$ range.

Now, to maximize his winning, Bradley should pick a number in the maximum probable range (i.e., $37-100$ range) and the number should be closer to Cathy's number and thus greater and closer to that of Albert. The closest number that can maximize his number after $37$ which is both greater and closer to it will be 38. So, the answer is $=\boxed{38}$

Since the number that Albert chose was 37, the number chosen by Bradley has to be 38. Then 63 numbers (38<=x<=100) would give him win.

First thing is that the probability of Cathy choosing a number is same for any number from 1-100. But probability that the number she chooses is greater than 37 is more than that of the number being less than 37. Therefore to maximize his chances of winning, Bradley should choose a number greater than 37. Also the number he chooses should be closer to the number Cathy chooses therefore the number he chooses should be 38.

There are more numbers between 37 and 100 than between 1 and 37. So there are more chances in the range of between 37 and 100. Choosing 38 all the numbers after it will benefit this choice. So, more numbers will near 38 than 37.

We only have to think a little... the numbers need to be between 1 and 100, inclusive, and Albert picked 37, so obviously if Bradley choose 38 he has more chance to win, cause he wins with any number between 38 and 100, inclusive, which gives more options than 1 to 37. No calculation need.

If the numbers chosen by Cathy were uniformly distributed, the answer is 38, as the other answers detail, because there are more integers to choose in the interval [38,100] than [1,36].

However, people are pretty bad random number generators! I think that the uniform distribution is a poor prior. It is an empirical question which of those intervals above would actually get picked more often by real people . Since we are more intimately familiar with numbers on [1,10] than numbers closer to 100, there's a good chance that the interval [1,36] could actually contain more statistical weight!

Do the experiment "choose a random number on [1,100]" with your friends and report back!

First thing is that the probability of Cathy choosing a number is same for any number from 1-100. But probability that the number she chooses is greater than 37 is more than that of the number being less than 37. Therefore to maximize his chances of winning, Bradley should choose a number greater than 37. Also the number he chooses should be closer to the number Cathy chooses therefore the number he chooses should be 38

It is 38 as the only way the Bradley could lose is if Cathy chose a number less than 37 and the chances were that this was unlikely. Thus, Bradley's choice helped maximise the chance of getting it right.

Think of a number line with 1 to 100. Albert is on 37. If albert is on 38 leaving numbers before 37, he can win for all 63 numbers.Any other place will have less numbers that he can win for.

1-37 range is smaller than 37-100 range. Bradly will have a larger chance of being closer to the number if he picks a number on the side of 37-100. However, if he randomly picks, he will be at an advantage because the distance from 37 to n could be equal to his number to n. He solves this problem by picking the next larger number, 38

38-100 has a larger chance of guessing the answer correctly than 1-37..

keep it simple.............

38(Albert picked 37. There are more numbers from 37-100 than 1-37; Bradely will have a larger chance of being closer to the number if he picks a number on the side of 37-100. However, if he randomly picks, he will be at an advantage because the distance from 37 to n could be equal to his number to n. He solves this problem by picking the next larger number, 38.)

bcz of the catchy says whoever chose max no his will get the basketball in the goal..

the number may be less than, equal or greater than 37. The possibility is greater that it is above 37 for there are as many as 63 such numbers till 100. So the number Bradley should pick is 38 so that any number greater than 37 will be closer to it.

38

yeah! i did solve it ^_^

We only have to think a little... the numbers need to be between 1 and 100, inclusive, and Albert picked 37, so obviously if Bradley choose 38 he has more chance to win, cause he wins with any number between 38 and 100, inclusive, which gives more options than 1 to 37. No calculation need.

37 is placed to the bracket 1-37 by the second guesser who gave number 38 which is from the bracket 38-100. Therefore, the bracket 38-100 (with 63 numbers) have more chance than the bracket 1-37 (with 37 numbers).

as the previous ones is 37, the next possibility for wiining the ball.. n0. must be between 38 to 100, if we choose the next no. of 37, then any no. after 38 will be the answer

Albert picked 37. There are more numbers from 37-100 than 1-37; Bradly will have more chance of being closer to the number if he picks a number on the side of 37-100. So he should chooses number 38

if cathy chooses the number 37 0r below 37 there are 37% chances of loosing ,by choosing 38 there are 63% chances of winning

if cathy chooses number less than 37 including 37 then definitely albert will be d winner and now as the second one who has to maximize his chances of winning the second one has to choose 38 as if cathy chooses number beyond 37 he will be the ultimate winner as he will be the nearer to it and now his chances of winning is 63% while for albert is 37%

Since Albert randomly guessed 37, you would have to see if there are more numbers from 1- 37 or 37- 100. Once you realize that you have to choose 38 the next number after 37 to make sure you will be closer to the answer than Albert.

38 .We assume that the event of the girl choosing any no is equally likely of her choosing any other . In that case each no has probability 1/100.Since 37 has been chosen .The total probability that the girl chose a no >37 =63/100 which is higher than the probability of her choosing a no<=37(37/100).So the guy will choose a no in the former region.Now to ensure that he wins if any no >37 is thought of he has to choose 38 because then it will be sure that if she chooses any no >37 he will be closer to it than the other guy.

1-37 have less numbers than 38-100 so the chances of getting write answer is greater

it is given that bradley has maximum chances. it means that the number picked by bradley is greater than Albert.and albert has choosen 37. and 38 is just greater than 37 which creates more chances of winning.

Since 37 was picked by Albert, Bradley picks 38. This is because there is a greater chance of Cathy selecting a number greater than 37 than a number less than it. Thus 38 would be one number closer than 37, to any number which comes in that range.

Since Albert chose 37, and Cathy picks a number randomly, the probability that her chosen number lies between 1-36 is 36%, and the probability that it lies between 38-100 is 73%. So Bradley must choose a number greater than 37 to maximize his chances. Now if he chooses a number x, such that 37<x<=100, then the probablity that his chosen number is closer to Cathy's is (100-(37+(x-37)/2). This is maximized when x=38.

i thought generally in a simple way that if albert picked a number is 37 then i thout a number should be > than from albert's number,so i picked up a number 38 & fortunately its correct.woww...amazing

The answer logically must be 38. If Bradley were to chose 38 then if Cathy's number was from 38-100 he would win. If he chose a number below 37 then 37 would win if the number was between 37-100 which the at most 36 possibilities would be less than 38-100. If it were 39 then 38 would be a tie which then there would be a tiebreaker. This lowers it by one possibility and going higher only makes it worse. If Bradley wants to obtain the best chance of winning he must have chosen 38.

It's very simple. To determine the number chosen by Bradley, we have to judge 2 things, (i)From which half the number should be chosen &(ii)At what distance from 37. Albert has chosen 37 which is less than 50, so in-order to increase his chances he will choose from the right half. Also to minimize the chances of loosing, he will choose a number next to 37. Thus, keeping both things in mind, Bradley will choose the number '38'. (Note:-->the term 'half' is used to depict the left{less than 37} & right{more than 37} side of the list 1-100 taking 37 as the central number)

Bradley should guess one of the integers that would be adjacent to the number Albert picked - as he picked 37, this would suggest either 36 or 38. There are more numbers where 38<B<100 than where 0<B<36, thus he should pick 38.