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Did you change the problem?
When I did 10 manually just now it came out to 5 open and 5 closed.
1 open
2 closed
3 closed
4 open
5 closed
6 open
7 closed
8 closed
9 open
10 open
0000000000
+0101010101
=0101010101
+0010010010
=0111010101
+0001000100
=0110010011
+0000100001
=0110110010
+0000010000
=0110100010
+0000001000
=0110100010
+0000000100
=0110101010
+0000000010
=0110101110
+0000000001
=110101100
When I did 10 manually just now it came out to 5 open and 5 closed.
1 open
2 closed
3 closed
4 open
5 closed
6 open
7 closed
8 closed
9 open
10 open
0000000000
+0101010101
=0101010101
+0010010010
=0111010101
+0001000100
=0110010011
+0000100001
=0110110010
+0000010000
=0110100010
+0000001000
=0110100010
+0000000100
=0110101010
+0000000010
=0110101110
+0000000001
=110101100
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- Thomas Pickert
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Yes, the algorithm has slightly changed.
1 = locked
0 = unlocked
1 = locked
0 = unlocked
Code: Select all
1111111111
+1111111111
=0000000000
+0101010101
=0101010101
+0010010010
=0111010101 <= error, correct: 0111000111
+0001000100
=0110010011
+0000100001
=0110110010
+0000010000
=0110100010
+0000001000
=0110100010
+0000000100
=0110101010
+0000000010
=0110101110
+0000000001
=110101100
- Thomas Pickert
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- kroner
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The answer for 100 accounts is 10. The answer for 10,000 accounts is 100. The perfect squares, which have an odd number of factors are flipped an odd number of times and therefore are open at the end. All the other numbers have an even number of factors and therefore stay closed. In general, for n accounts, the number open at the end is the greatest integer less than or equal to the square root of n.
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