Problem 321

[LarryBlake]

Problem 321 (View Problem)
Can a counter jump another counter of the same color?

[GenePeer]

Whichever the case, I doubt it would provide the optimal solution.

This is the first "new" problem I have tried, as I prefer solving sequentially. I'm currently at 103. I've found a formula for the number of moves needed, and was able to generate the first 22 terms. It could take days if I continued like this. Can someone hint me in the right direction?

[stijn263]

Can you perhaps spot a pattern among those first 22 terms?

Have fun solving!

[GenePeer]

Why did I think there's no possible pattern? Thank you, I just had my first post in an unarchived thread.

[sivakd]

GenePeer, congratulations. I just noticed that you are the only person from your country. So, a good achievement indeed.

Why did I think there's no possible pattern? Thank you, I just had my first post in an unarchived thread.

[john.schooling]

I get 5=99, 10=8108, 20=54608372. Can anyone confirm this is correct please. My answer to 40 terms is incorrect. I may have a rounding or overflow problem.
Thanks.

[jaap]

Those numbers are correct.

[gotclout]

I get 5=99, 10=8108, 20=54608372. Can anyone confirm this is correct please. My answer to 40 terms is incorrect. I may have a rounding or overflow problem.
Thanks.

I'm having a similar issue, however I'm making a first attempt to solve this in python and I'm not sure if the problem could be rounding or overflow.

[ingreenheaven]

Why did I think there's no possible pattern? Thank you, I just had my first post in an unarchived thread.

I can't see the pattern

[ingreenheaven]

My answer for 20 matches with the answers above, but my final answer is not correct. Can somebody verify if these values are correct. 25: 636562052 and 30: 1583407950?

Also any push in the right direction for identifying the pattern will be very helpful.

[jaap]

My answer for 20 matches with the answers above, but my final answer is not correct. Can somebody verify if these values are correct. 25: 636562052 and 30: 1583407950?

No. You probably have a 32 bit integer overflow problem. You need 64 bit integers.

[ingreenheaven]

My answer for 20 matches with the answers above, but my final answer is not correct. Can somebody verify if these values are correct. 25: 636562052 and 30: 1583407950?

No. You probably have a 32 bit integer overflow problem. You need 64 bit integers.

Thank you.

[ingreenheaven]

Done. It was a problem with precision. The pattern that I thought was there didn't work because of precision error and so I thought I was missing something. Thanks for your help.

[DeEiserne]

There's something I don't quite understand:
If we take n=2, then we have 2 red, 2 blue counters. Let's just write the configuration as 1 2 3 4 5 , where 1 and 2 are initially occupied by the 2 red counters, etc. For n=2, there is a solution with 8 actions:

2 -> 3
4 -> 2
5 -> 4
3 -> 5
1 -> 3
2 -> 1
4 -> 2
3 -> 4

M(1) is clearly 3 and M(3) is clearly 15, so according to the problem's description, M(2) should be 10. But M(2) is 8 (see above) and 8 is clearly not a triangle number.
What am I doing wrong?

[mpiotte]

There's something I don't quite understand:
If we take n=2, then we have 2 red, 2 blue counters. Let's just write the configuration as 1 2 3 4 5 , where 1 and 2 are initially occupied by the 2 red counters, etc. For n=2, there is a solution with 8 actions:

2 -> 3
4 -> 2
5 -> 4
3 -> 5
1 -> 3
2 -> 1
4 -> 2
3 -> 4

M(1) is clearly 3 and M(3) is clearly 15, so according to the problem's description, M(2) should be 10. But M(2) is 8 (see above) and 8 is clearly not a triangle number.
What am I doing wrong?

You misread the question. Nowhere is the value of M(2) provided. The problem statement gives that M(3) = 15 and that M(1), M(3), M(10), M(22) and M(63) are triangular numbers (without giving the value).

[DeEiserne]

Oh my god, I feel so stupid. Thank you for the clarification!

[Jochen_P]

Can you perhaps spot a pattern among those first 22 terms?

Have fun solving!

hmm ... pattern spotting ... 1,3,10,22,63,1nn,3nn
Nope, don't see any. Any hint?

Got the same results as others for 20(correct), 25(false) and 30(false)

[Jochen_P]

Got it ... very nice pattern, not easy to spot