I was doing this problem on Spoj. The solution of this problem is that first player always wins.
Can anyone give me proof of this?
# | User | Rating |
---|---|---|
1 | jiangly | 3640 |
2 | Benq | 3593 |
3 | tourist | 3572 |
4 | orzdevinwang | 3561 |
5 | cnnfls_csy | 3539 |
6 | ecnerwala | 3534 |
7 | Radewoosh | 3532 |
8 | gyh20 | 3447 |
9 | Rebelz | 3409 |
10 | Geothermal | 3408 |
# | User | Contrib. |
---|---|---|
1 | maomao90 | 173 |
2 | adamant | 164 |
3 | awoo | 162 |
4 | TheScrasse | 160 |
5 | nor | 159 |
6 | maroonrk | 156 |
7 | SecondThread | 154 |
8 | pajenegod | 147 |
9 | BledDest | 145 |
9 | Um_nik | 145 |
Name |
---|
Proof by contradiction :
Say the initial state is always a losing state. This means regardless of the number the first player picks , the second player ends up with a winning state (if not , the initial state would have been a winning state). Say the first player picks 1 and the second player ends up with {2,3,4,.....,N} which is a winning state. Say the second player picks X now and provides the first player with state S (a losing state) , the first player could have just picked X and forced the second player to state S ( a losing state) which is a contradiction. Hence the first player always wins.
Thanks.. :))