Mixing
Combinatorics game problem
$begingroup$
Two people, Alice and Ben, take turns removing marbles from a bag. The bag contains $1$ purple, $1$ orange, $4$ green, $6$ red and $2^8$ blue marbles. If Alice starts, at least one marble must be taken out on each turn and no more than one marble of the same color can be taken out on each turn, who removes the last marble? (whoever removes the last marble wins)
combinatorics
edited Jan 30 at 23:17
abc...
3,237739
asked Jan 30 at 22:42
IrinaIrina
11
$endgroup$
add a comment |
$begingroup$
Two people, Alice and Ben, take turns removing marbles from a bag. The bag contains $1$ purple, $1$ orange, $4$ green, $6$ red and $2^8$ blue marbles. If Alice starts, at least one marble must be taken out on each turn and no more than one marble of the same color can be taken out on each turn, who removes the last marble? (whoever removes the last marble wins)
combinatorics
edited Jan 30 at 23:17
abc...
3,237739
asked Jan 30 at 22:42
IrinaIrina
11
$endgroup$
add a comment |
$begingroup$
Two people, Alice and Ben, take turns removing marbles from a bag. The bag contains $1$ purple, $1$ orange, $4$ green, $6$ red and $2^8$ blue marbles. If Alice starts, at least one marble must be taken out on each turn and no more than one marble of the same color can be taken out on each turn, who removes the last marble? (whoever removes the last marble wins)
combinatorics
edited Jan 30 at 23:17
abc...
3,237739
asked Jan 30 at 22:42
IrinaIrina
11
$endgroup$
Two people, Alice and Ben, take turns removing marbles from a bag. The bag contains $1$ purple, $1$ orange, $4$ green, $6$ red and $2^8$ blue marbles. If Alice starts, at least one marble must be taken out on each turn and no more than one marble of the same color can be taken out on each turn, who removes the last marble? (whoever removes the last marble wins)
combinatorics
combinatorics
edited Jan 30 at 23:17
abc...
3,237739
asked Jan 30 at 22:42
IrinaIrina
11
edited Jan 30 at 23:17
abc...
3,237739
asked Jan 30 at 22:42
IrinaIrina
11
edited Jan 30 at 23:17
abc...
3,237739
edited Jan 30 at 23:17
abc...
3,237739
edited Jan 30 at 23:17
abc...
3,237739
3,237739
asked Jan 30 at 22:42
IrinaIrina
11
asked Jan 30 at 22:42
IrinaIrina
11
asked Jan 30 at 22:42
IrinaIrina
11
11
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Alice removes the last marble. Take the purple and the orange out first, then apply copycat strategy: take out whatever marble(s) Ben took on his last turn. This guarantees Alice to take the last marble since the parity of all colours marbles are even.
answered Jan 30 at 23:16
abc...abc...
3,237739
$endgroup$
$begingroup$
So Alice takes two at a time each time?
$endgroup$
– Irina
Jan 30 at 23:35
$begingroup$
Not necessarily. She takes whatever amount Ben takes, and of the same color.
$endgroup$
– abc...
Jan 31 at 0:39
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Alice removes the last marble. Take the purple and the orange out first, then apply copycat strategy: take out whatever marble(s) Ben took on his last turn. This guarantees Alice to take the last marble since the parity of all colours marbles are even.
answered Jan 30 at 23:16
abc...abc...
3,237739
$endgroup$
$begingroup$
So Alice takes two at a time each time?
$endgroup$
– Irina
Jan 30 at 23:35
$begingroup$
Not necessarily. She takes whatever amount Ben takes, and of the same color.
$endgroup$
– abc...
Jan 31 at 0:39
add a comment |
$begingroup$
Alice removes the last marble. Take the purple and the orange out first, then apply copycat strategy: take out whatever marble(s) Ben took on his last turn. This guarantees Alice to take the last marble since the parity of all colours marbles are even.
answered Jan 30 at 23:16
abc...abc...
3,237739
$endgroup$
$begingroup$
So Alice takes two at a time each time?
$endgroup$
– Irina
Jan 30 at 23:35
$begingroup$
Not necessarily. She takes whatever amount Ben takes, and of the same color.
$endgroup$
– abc...
Jan 31 at 0:39
add a comment |
$begingroup$
Alice removes the last marble. Take the purple and the orange out first, then apply copycat strategy: take out whatever marble(s) Ben took on his last turn. This guarantees Alice to take the last marble since the parity of all colours marbles are even.
answered Jan 30 at 23:16
abc...abc...
3,237739
$endgroup$
Alice removes the last marble. Take the purple and the orange out first, then apply copycat strategy: take out whatever marble(s) Ben took on his last turn. This guarantees Alice to take the last marble since the parity of all colours marbles are even.
answered Jan 30 at 23:16
abc...abc...
3,237739
answered Jan 30 at 23:16
abc...abc...
3,237739
answered Jan 30 at 23:16
abc...abc...
3,237739
answered Jan 30 at 23:16
abc...abc...
3,237739
3,237739
$begingroup$
So Alice takes two at a time each time?
$endgroup$
– Irina
Jan 30 at 23:35
$begingroup$
Not necessarily. She takes whatever amount Ben takes, and of the same color.
$endgroup$
– abc...
Jan 31 at 0:39
add a comment |
$begingroup$
So Alice takes two at a time each time?
$endgroup$
– Irina
Jan 30 at 23:35
$begingroup$
Not necessarily. She takes whatever amount Ben takes, and of the same color.
$endgroup$
– abc...
Jan 31 at 0:39
$begingroup$
So Alice takes two at a time each time?
$endgroup$
– Irina
Jan 30 at 23:35
$begingroup$
So Alice takes two at a time each time?
$endgroup$
– Irina
Jan 30 at 23:35
$begingroup$
Not necessarily. She takes whatever amount Ben takes, and of the same color.
$endgroup$
– abc...
Jan 31 at 0:39
$begingroup$
Not necessarily. She takes whatever amount Ben takes, and of the same color.
$endgroup$
– abc...
Jan 31 at 0:39
add a comment |
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