Solving the Stacking Squares mind teaser:

There are 5 Squares, each one smaller than the next. The object is to move one square at a time and re-stack them on another pin. But there are 3 Simple Rules to follow.

Rule #1. Move only one square at a time.

Rule #2. Cannot put a larger square on top of smaller square.

Rule #3. Cannot move a stack of squares at once to another pin. See Rule #1.

The key to solving this puzzle is in its name "Stacking Squares" which is what you will be doing as you complete it.


The table below shows how to solve it in 31 moves:
The smallest Square is A. Next bigger is B, C, D and E is the largest square of all.

First, place the board so all Pins are parallel to you, Pin 1 is on the left. Second, place all the squares (stack them up) starting with the largest E,  then D, C, B, A on Pin1 .  (After you get familiar with solving it you can place the squares on any Pin.)

In the table below: Each Row (across) is one move. So for Move 1 you will place Square A, the smallest on Pin 3 which should be the right most Pin. Move 2 is placing Square B on Pin 2 (the middle pin). Move 3 is placing Square A on top of Square B on the middle Pin and so forth. So after 3 moves Square A and B should be on Pin 2, with B on the bottom. Notes, below show periodically where the Squares should be after that move.
Good Luck!
Or... download the solution in a .pdf file.

Move Pin 1 Pin 2 Pin 3 Notes See Pic of this move
Start ABCDE Start
1 A Move 1
2 B Move 2
3 A Move 3
4 C Move 4
5 A Move 5
6 B Move 6
7 A Squares ABC should be on Pin 3 Move 7
8 D Move 8
9 A Move 9
10 B Move 10
11 A Move 11
12 C Move 12
13 A Move 13
14 B Move 14
15 A Move 15
16 E Squares ABCD should be Pin 2 and Square E on Pin 3 Move 16
17 A Move 17
18 B Move 18
19 A Move 19
20 C Move 20
21 A Move 21
22 B Move 22
23 A Move 23
24 D Squares ABC on Pin 1, Squares DE on Pin 3 Move 24
25 A Move 25
26 B Move 26
27 A Move 27
28 C Move 28
29 A Move 29
30 B Move 30
31 A Congratulations! all Squares should be on Pin 3 Move 31

Interesting Note:

You will notice a repeating pattern above. Square A is moved every other move. Square B is moved every 4 moves. C is moved every 8 moves and although D is moved on the 8 move its not moved again for 16 moves. With 3 pegs you can only move a square to one of the other two pegs which is why the moves are divisible by 2. And why each larger square is only moved half the number of moves of it's next smaller square. 16, 8, 4, 2.

Also Square A, if first moved to the far right peg first, moves to its left and then left again and then back to far right and repeats. Square B moves in the opposite direction and repeats. C moves the same direction as A and D as B, But according to their Double. Since the puzzle is solved in 31 moves, the other Squares don't repeat as often. D is moved only twice and E moved only once.

So if Square A moves 16 times and B moves 8 times and C 4, D 2, and E once then the number of moves is 16 + 8 + 4 + 2 + 1 = 31.

Also which ever Pin you start Square A on is where the rest of the squares will end up when you are finished. You can therefore solve the puzzle just by following the pattern of each Square. Square A has to move every other move. Square B every 4 moves and so forth.

Enjoy solving the Puzzle, Doogie. email me:    Doogie @ doogiestoyshop . com  (Please copy and paste this email without spaces).