[bonanova]

You have 16 coins in a 4x4 array, numbered 1-16: 1-4 is top row, etc.

When you touch a coin, it flips, along with the other coins in its row and column; 7 coins in all flip.

The objective is to make all the coins show tails in the fewest possible moves.

For graphical clarity, O is heads, + is tails.

Here's an easy example: coins 4, 7, 10 and 13 are heads.

+ + + O

+ + O +

+ O + +

O + + +

Touching coin 4 produces this array:

O O O +

+ + O O

+ O + O

O + + O

It's easy to verify that touching coins 7, 10 and 13, in any order, then completes the task of getting all tails [+]'s.

The solution thus would be written 4 7 10 13. Or 4 10 13 7.

Order of moves does not matter.

Flip all sixteen coins to tails [+] in the fewest moves possible:

Puzzle 1 [easy]

O O O O

O + O O

O O + O

O O O O

Puzzle 2 [harder]

O O O +

O O O O

O + O O

O O O O

Have fun.

[Prime]

Reusing what Bonanova has already given away,

The {1,16} moves convert the position in puzzle 1 into the initial example in the OP (the zero diagonal). From there, Bonanova has already given the moves: {4,7,10,13}.

So, {1,16,4,7,10,13} it is.

[Guest]

Test it out your solution here.

[Guest]

Puzzle 1: 1,4,7,10,13,16

Puzzle 2: 2,5,7,12,13,15

[bonanova]

Puzzle 1: 1,4,7,10,13,16

Puzzle 2: 2,5,7,12,13,15

Six moves is minimum - nice.

That page is new to me - did you construct it?

[Guest]

That page is new to me - did you construct it?

Yes, you can create any webpage free at weebly.com. It's quite convenient.