Proof of puzzle with n pieces

[lookingforhelp]

Hey guys, still new here, so I hope this is in the right category.
There is a puzzle with n pieces. The puzzle is assembled by a series of moves- you can either add a piece to an assembled block or put together two blocks of assembled pieces. The final move would be to put together two blocks. Using strong induction, prove that it will take exactly n-1 moves to assemble the puzzle.

What I have so far, not sure if it's correct...
Proof: By strong induction
Let n= number of pieces of puzzle
Case n=1: 0 moves to assemble
Case n=2: 1 move to assemble (assemble two blocks)
Assume true for n=1,2,3....,k-1
Goal: Show for n=k
???

Thanks for any help!

 

[HallsofIvy]

Hey guys, still new here, so I hope this is in the right category.
There is a puzzle with n pieces. The puzzle is assembled by a series of moves- you can either add a piece to an assembled block or put together two blocks of assembled pieces. The final move would be to put together two blocks. Using strong induction, prove that it will take exactly n-1 moves to assemble the puzzle.

What I have so far, not sure if it's correct...
Proof: By strong induction
Let n= number of pieces of puzzle
Case n=1: 0 moves to assemble
Case n=2: 1 move to assemble (assemble two blocks)
Assume true for n=1,2,3....,k-1
Goal: Show for n=k
???

Thanks for any help!

Assuming "it takes n-1 moves to assemble n pieces" is true for n= 1, 2, 3, ..., k- 1, let i be an integer less than k. It will take i- 1 moves to assemble a block of i pieces. It will take k- i- 1 moves to assemble the other k- i pieces. The last move is assembling those two blocks. That is total of (i- 1)+ (k- i- 1)+ 1= k- 1 moves to assemble all k pieces. (This is assuming that any set of i pieces can be assembled into a block.)