Sliding coins

Logic Level 3

What is the minimum number of moves required to change the arrangement at the left to the right consisting of 15 coins by sliding one coin at a time to a different position in which it touches two other coins?

Note: Generalize this.

Details And Assumptions :

  • Neglect the design inscribed on the coin and consider all coins to be plain.
  • You cannot lift the coins.
4 7 6 5 3 8

Nihar Mahajan by Nihar Mahajan , 20, India

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2 solutions

Nihar Mahajan
Jul 1, 2015

In the image , let the red circles be touching.

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Moderator note:

Can you prove that it's minimum? Hint: See Prasun Biswas' note .

Ahmed Obaiedallah
Jul 11, 2015

Well to solve this kind of problems I try first to determine the part that won't move and I found out in such problems it's a hexagon core (regular or irregular) ,

Then I just pop the moving parts out and kind of imagine myself rotating them around a circle then push them back in their new position

Here is another one with bigger triangle (28 coins) that has a regular hexagon in it's core (because it's more understandable with a regular hexagon core)

Also notice the inner 10 coins triangle it has a regular hex core as well I gave it a different color so you can recognize it easily

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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