Two bags each contain 3 red, 3 white and 3 blue marbles. Without looking, someone removes from the first bag the LARGEST number of marbles that it is possible to remove while still being sure that at least one of each colour remains. These marbles are put into the second bag. He now transfers back (without looking of course) the SMALLEST possible number of marbles that will assure there being at least 2 of each colour in the first bag.
How many marbles remain in the second bag?
2006-08-14 21:40:11 · 24 answers · asked by brainyandy 6 in Science & Mathematics ➔ Mathematics
No correct answers yet!
2006-08-14 22:34:32 · update #1
it's 4.
the maximum no. you can take from the 1st bag is 2 to avoid getting 3 of a kind.
that leaves 11 marbles in the 2nd bag.
the least no. you can take from the 2nd bag is 7 to assure that you get atleast one of each kind.
that gives each color a pair in the 1st bag.
the answer is 4.
2006-08-15 02:08:43 · answer #1 · answered by Anonymous · 1⤊ 0⤋
The first time he removes 2, as he cannot look he has to take out 2 as if he took out 3 and they were all the same colour then that colour would no longer be in the bag.
The second time he removes 7, as he cannot look he has to take out 7 as if he took 6 then if the first time both were the same colour then the 6 could be 3 of each of the two other colours, therefore only making 1 marble of the colour he picked out first in the first back.
If there are 11 marbles in the second bag after the first transfer (3*3 = 9 due to 3 red,white and blue) then an extra 2 because 2 were added afterwards.
Then there would be 4 at the end (11 - 7 which he transferred back to the first bag).
Therefore there are 4 left in the second bag.
2006-08-15 03:06:16 · answer #2 · answered by Anonymous · 1⤊ 0⤋
Sorry, it should be 16 marbles in first bag, 2 marbles in 2nd bag.
To take maximum amount without looking and still ensure that there is at least one of each color is 2. (taking 3 has the possibility of remove all of 1 color). So at this point, bag 2 will have 9 + 2 = 11 marbles. For the transfer back, one needs to take a minimum of 9 marbles, 5 (3+2) + 3 + 1 to ensure that the mix have at least 1 of each color and put them back into bag1. So total will be 7 (2 previously removed) + 9 = 16 and 2 marbles left in 2nd bag.
2006-08-14 23:28:52 · answer #3 · answered by ali 6 · 0⤊ 0⤋
He would remove 2 marbles from the first bag and place in the second bag. The remaining colors will be 3+3+1 or 3+2+2
The number of marbles will be 5+3+3 or 4+4+3 = 11.
To ensure he takes out at least 1 marble of each color added, he must take out 7 (3+3+1) marbles in case 1 or 8 (3+4+1) marbles in case 2 from the second bag. Therefore 8 marbles must be taken out.
11 - 8 = 3 marbles left in second bag
2006-08-14 22:03:56 · answer #4 · answered by Anonymous · 2⤊ 0⤋
3
From the first bag a maximum of 2 marbles was removed. Because if we remove three they could be from the same colour.
now the two marbles were put in the second bag.
We need to bring marbles back to the first bag so that at least 2 of each colour are there. It is possible that we have 1 marble of a certain colour in the first bag while in the second bag we have 3,4,4. if we take the first 3 will, it is not working, now we take the four, it is still not working and at leat we need one marble from the last 4 to satisfy the condition. therefore only three remain in the second bag
2006-08-14 21:54:45 · answer #5 · answered by Clinkit 2 · 1⤊ 0⤋
The answer is 10 Marbles.
As there are 3 marbles of each colour in each bag, the largest number of marbles that can be removed from the first bag to be sure of leaving one of each colour is 2.
There are now 11 marbles in the second bag.
The smallest number of marbles that can be removed from the second bag to leave 2 of each colour is 1.
Thus leaving 10 marbles.
2006-08-15 02:52:19 · answer #6 · answered by Anonymous · 0⤊ 0⤋
3
2006-08-14 21:42:17 · answer #7 · answered by Anonymous · 0⤊ 0⤋
And if you drop the two bags and the contents run down the drain you will have lost your marbles!
To be CERTAIN that one of each colour remains, you can only take out 2 marbles (2 red leaves 3 white, 3 Blue and 1 Red)
After this, you only need to return 1 marble to be CERTAIN that 2 of each are in the first bag.
2006-08-14 21:50:47 · answer #8 · answered by Tony T 3 · 1⤊ 0⤋
4.
As you can see he can only pick two because if he picks three there is a possibility that he can pick 3 marbles of the same colors. There are now 11 marbles in the second bag.
Now there is a possibility that there are 5 marbles in the second bag of the same color. He must then pick 7 (get 3 marbles, 3 from another color and at least one for the 5-,marble color).
The answer is 4.
Right?
^_^
2006-08-15 00:32:26 · answer #9 · answered by kevin! 5 · 1⤊ 0⤋
There remains 1 marble. The largest possible number is two, because if you remove three, they could all be one colour. So theres two in the second bag, you can only rfemove one, so that you know that there are two of each colour in the first bag, that leaves one in the second bag.
2006-08-14 22:06:56 · answer #10 · answered by Anonymous · 0⤊ 0⤋