Of these US Coins (Quarter and Dime Combo).

Initial arrangement of the coins as shown in the picture is as follows... Q D Q D Q D Q

Objective is to attain the final configuration... Q Q Q Q D D D.


You are allowed to move a pair of coins (QD or DQ) as a unit .

You have to place them in the same configuration(DQ or QD) between any coin, front or at the end of the row.

You have to repeat the process till final desired configuration is reached.

Document the intermediate steps and any particular strategy employed.

enter image description here

  • $\begingroup$ Please ignore my previous comments..I will accept the solution as given $\endgroup$ – Uvc Jun 23 at 18:52

I can do it in

3 Steps

Basically, working from the front

Grab the first pair (QD), move it to the end (QDQDQQD)
Grab the second pair (QD) from the front, move it to between the last two coins (QDQQQDD)
Grab the third pair (QD) from the fron, move it to between the last quarter and first dime (QQQQDDD).

  • $\begingroup$ Forgot to add..it cannot touch the same coin in the row..I can edit $\endgroup$ – Uvc Jun 23 at 18:41
  • $\begingroup$ Please ignore my comment..will accept the solution $\endgroup$ – Uvc Jun 23 at 18:52
  • $\begingroup$ My solution was long winded..yours is much simpler $\endgroup$ – Uvc Jun 23 at 18:56

Let’s start with notation:

^ will indicate where I want to insert, bold font will indicate what’s being moved.

I just tried to

Force the DQs to fit between other DQs, creating a pattern of DDQQs that could easily be moved.

  • $\begingroup$ In the third, d is in front of the moved unit DQ..not allowed.. $\endgroup$ – Uvc Jun 23 at 18:46
  • $\begingroup$ Please see my edit..if further clarification is needed, I will provide. $\endgroup$ – Uvc Jun 23 at 18:47
  • $\begingroup$ Please ignore my comment $\endgroup$ – Uvc Jun 23 at 18:53

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