# 15.1 variant 7: Towers of Hanoi with 2n disks that are black or white

#1

In the initial state of the pegs, before I move any disks, can I assume that the black and white disks already conform to the problem constraint that no white ring can be directly on top of a black disk?

If so, doesn’t that imply that it’s always the case that disks are grouped by color and the white group is always below the black group?

Thanks!

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#2

Yes, it will group by color.

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#3

Thanks.

Further clarification -

(1) Is it possible for the initial state to only contain all black or all white rings? Or is it always a mix?

(2) Is it allowed for the solution to traverse the rings on a peg to see all the colors, without actually removing any ring from the peg? In other words, do this without the traversal counting towards the number of ring-move operations. Or does each ring have to be removed from the peg to see its color?

Thanks!

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#4

Initial state has to be legal, and you can count the colors in a peg for sure but the only constraint is how you moving ring.

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#5

Thanks @tsunghsienlee. So it’s legal for initial state to contain only, for example, black disks?

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#6

The solution to this variant is so simple and straightforward compared to the others that it doesn’t require recursion. I would suggest cutting this problem from future editions.

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#7

Thanks for the suggestion, and we are still thinking how to incorporate variants into the new EPI judge as we do want to let readers to practice on variants as well.

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#8

Clarification please - are the 2n disks of the same size? Or are they 2n disks of 2n different sizes with top n disks being black and bottom n disks being white?

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