| ??? 10/05/11 08:14 Modified: 10/05/11 09:04 Read: times |
#184045 - Many patterns complex/hard to enter Responding to: ???'s previous message |
You can't have two lines through a point. You can attach to the point and optionally continue to next point. But in the end, you have a "traveling salesman" that optionally don't have to visit all cities.
1 point = C(1,1)*1! 2 points = C(2,1)*1! + C(2,2)*2! 3 points = C(3,1)*1! + C(3,2)*2! + C(3,3)*3! ... where C(n,m) is binominal coefficient = n! / (m!*(n-m)!) 1 point = 1*1 = 1 2 points = 2*1 + 1*2 = 4 3 points = 3*1 + 3*2 + 1*3 = 15 4 points = 4*1 + 6*2 + 4*6 + 1*24 = 64 size 1 = 1 size 2 = 4 size 3 = 15 size 4 = 64 size 5 = 325 size 6 = 1,956 size 7 = 13,699 size 8 = 109,600 size 9 = 986,409 size 10 = 9,864,100 size 11 = 108,505,111 size 12 = 1,302,061,344 size 13 = 16,926,797,485 size 14 = 236,975,164,804 size 15 = 3,554,627,472,075 size 16 = 56,874,039,553,216 The bad thing here is that while the combinations increases rapidly, many of them are very uncomfortable to enter. I wonder if the number of "good" combinations can be expressed in a good way. Edit: corrected formula Edit: Added evaluated results. |
| Topic | Author | Date |
| A quick question | 01/01/70 00:00 | |
| Many patterns complex/hard to enter | 01/01/70 00:00 | |
| oohh | 01/01/70 00:00 | |
| 9 points grid (3x3) 4lines ? | 01/01/70 00:00 | |
| Yes and no | 01/01/70 00:00 | |
| 3x3 grid in real life | 01/01/70 00:00 | |
| Not at all - goal is security, not puzzle | 01/01/70 00:00 | |
| Only one way to to connect 3x3 with 4 lines | 01/01/70 00:00 | |
| Stupid | 01/01/70 00:00 | |
| Stupid opinion | 01/01/70 00:00 | |
| Yes, I do know the solution | 01/01/70 00:00 | |
| Patterns ... | 01/01/70 00:00 | |
| No time. No acceleration. No lift. No finger outside screen. | 01/01/70 00:00 | |
Password Glyphs | 01/01/70 00:00 |