Karroth's answer is correct. Your logic, sunyujie, is obviously wrong because the sum of your probabities is greater than 1, which is impossible. Probabilities must = 1.

Anyone who can't quite accept the logic of this can test it very simply and easily with an ace and a pair of twos from any pack of cards. Pick a card, then discard a two, and then note whether staying or switching would get you the ace. Repeat 30 times and you will see that switching does indeed get you the ace twice as often.

sunyujie wrote:when host reveals a door, there is a t shirt, so your chances are increased to 66%

I don't quite see the logic in this statement. Could you explain?

sunyujie wrote:if you switch, you have a 50-50 chance

Same goes for this one.

I think a week with no new riddle is long enough for me to post another one.

Here goes:

What is the smallest positive number evenly divisible (divisible with no remainder) by all the natural numbers 1 through 20?

If you need a place to start, the smallest number evenly divisible by numbers 1 - 10 is 2520.

There is a simple mathematical method to solve this; I figured it out with a pencil, paper, and a four function calculator. However you solve it, though, include an explanation with your answer.

21, 162, 960

List the prime factors of each number.

2 1 x 2
3 1 x 3
4 2 x 2
5 1 x 5
6 2 x 3
7 1 x 7
8 2 x 2 x2
9 3 x 3
10 2 x 5
11 1 x 11
12 2 x 2 x 3
13 1 x 13
14 2 x 7
15 3 x 5
16 2 x 2 x 2 x 2
17 1 x 17
18 2 x 3 x 3
19 1 x 19
20 2 x 2 x 5

Then, multiply each factor the most number of times that it occurs in any single set of factors. eg. 2 occurs 4 times in 16 so you use 2 four times.

You end up with 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 11 x 13 x 17 x 19 = 21, 162, 960

Huh. Your logic is right, and your method makes sense, but you didn't get the right number.

2x2x2x2x3x3x5x7x11x13x17x19 doesn't equal 21,162,960. Looks like you left out the 11.

21,162,960 x 11 = 232,792,560 , which is the right answer.

The way I looked at it is that you can take every prime that is less than 20, and raise it to the highest power that is also less than 20.

2^4 is 16 (2^5 would be 32, which is more than 20), 3^2, 5^1, 7^1, etc.

In any case, nice job.

not good at math

dang think we should just do another riddle maybe one without so much math

sry didnt read that one my bad umm loose change