Flip swap skip

 Puzzle

Nice — here’s a little “Flip / Swap / Skip” puzzle pack for you. Rules first, then three puzzles (easy → hard). I’ll show solutions for the easy and hard ones so you can try the medium if you want.

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Rules (operations)

Starting from a row of tiles (left → right). allowed moves:

Flip — reverse the entire row.

Example: 1 2 3 4 5 → 5 4 3 2 1.

Swap i‑j — swap adjacent tiles at positions i and i+1 (I’ll write it as swap i-(i+1); positions are 1‑based).

Example: 1 2 3 4 5 → 1 **3 2** 4 5 after swap 2-3.

Skip — take the leftmost tile and move it to the right end (a one-step left rotation).

Example: 1 2 3 4 5 → 2 3 4 5 1.

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Puzzle 1 — Easy

Start: 1 2 3 4 5

Target: 2 1 3 4 5

Goal: reach the target in as few moves as possible.

Solution (minimal): swap 1-2

Steps: 1 2 3 4 5 → 2 1 3 4 5.

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Puzzle 2 — Medium (try it!)

Start: 1 2 3 4 5

Target: 3 4 5 1 2

(think about using Skip a couple times — don’t peek if you wanna solve it!)

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Puzzle 3 — Hard (I’ll give the minimal solution)

Start: 1 2 3 4 5

Target: 2 5 3 1 4

Find the shortest sequence of allowed moves.

Minimal solution (4 moves):

1. skip

2. swap 3-4

3. swap 2-3

4. swap 4-5

Step-by-step:

Start: 1 2 3 4 5

After skip: 2 3 4 5 1

After swap 3-4 (swap positions 3 & 4): 2 3 5 4 1

After swap 2-3 (swap positions 2 & 3): 2 5 3 4 1

After swap 4-5 (swap positions 4 & 5): 2 5 3 1 4 ✅

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Want more puzzles like this (larger size, different allowed moves, or make it a shortest‑moves

 competition)? Or do you want me to generate a random scramble and time you? 😄