<p>The solution is for white to move their row of 3 one space forward. There are a bunch of possible moves for black but white can guarantee a win from all of them.</p>

<p><a href="https://i.sstatic.net/mna1g.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/mna1g.png" alt="enter image description here"></a></p>

<h1>If black moves away from their back line:</h1>

<p>If black moves their leftmost piece away from the line, then red pushes forward. Black is forced to use their remaining 2 to capture red, who captures again. Black can't capture the remaining piece.</p>

<p><a href="https://i.sstatic.net/SwqjM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/SwqjM.png" alt="enter image description here"></a></p>

<p>This is similar to the situation with the rightmost piece:</p>

<p><a href="https://i.sstatic.net/LzLpb.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/LzLpb.png" alt="enter image description here"></a></p>

<p>If black moves the middle piece away, then they will have to reform the broken 2 in order to defend the back line. Red aims a phalanx there:</p>

<p><a href="https://i.sstatic.net/7oCbM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7oCbM.png" alt="enter image description here"></a></p>

<p>If black moves the middle piece to the side to avoid this diagonal phalanx, red goes too far away on the other side:</p>

<p><a href="https://i.sstatic.net/lDi3B.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/lDi3B.png" alt="enter image description here"></a></p>

<h1>If black stays on the back line</h1>

<p>If black is staying on the back line, then their first move cannot be to the left. Any distance to the left allows red to take the first capture and keep pushing to win. Thus black moves right. If black moves more than one space to the right, then they're too far away to defend from the single piece moving in. If black moves one space to the right, red forces the black row to capture their piece, lining up the black phalanx to be split in half:</p>

<p><a href="https://i.sstatic.net/UoNe5.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/UoNe5.png" alt="enter image description here"></a></p>

CC BY-SA 3.0
2016-02-02T11:19:03.147Z
That said, this question is probably more suited to the [Puzzling Stack Exchange](http://puzzling.stackexchange.com).
Samthere
CC BY-SA 3.0
2016-02-02T11:48:31.593Z
And probably this answer is oversimplified - I've been playing with having black make the best defensive move each time and it's tough!
Samthere
CC BY-SA 3.0
2016-02-02T11:50:03.613Z
You cannot choose how black moves; you should show that it cannot play in any way so as to prevent the win by white. Also to win white only needs one of its pieces on black's back rank (since black is nowhere near white's back rank).
hkBst
CC BY-SA 3.0
2016-02-02T12:04:10.253Z
@hkBst Right! I think I've got it, just working through the possibilities.
Samthere
CC BY-SA 3.0
2016-02-02T13:45:09.473Z
@hkBst Okay, I worked it out over lunch with some board game parts :P I'll write it up now!
Samthere
CC BY-SA 3.0
2016-02-02T15:12:59.777Z
From [the help](http://boardgames.stackexchange.com/help/on-topic): "Questions about Go problems or Chess problems are fine, even if they are static puzzles, since they are related to a dynamic game." Can be extended to Epaminondas so this question is certainly on-topic here (as well as on Puzzling).
freekvd
CC BY-SA 3.0
2016-02-02T15:14:06.417Z
NOPE I GOT IT WRONG AGAIN AAAAAAAAAAAAAAAAAAAAAAAAAAARGH
Samthere
CC BY-SA 3.0
2016-02-02T15:26:36.337Z
Okay, I've actually got it! Finishing this up.
Samthere
CC BY-SA 3.0
2016-02-02T20:21:17.780Z
I don't think these 'forced captures' are mandatory, sorry.
freekvd
CC BY-SA 3.0
2016-02-03T08:07:55.517Z
If the middle black piece moves out of line, red can immediately move forwards for a win, because black cannot recapture.
hkBst
CC BY-SA 3.0
2016-02-03T08:20:31.463Z
@hkBst Right you are, but I this way gets a win in exactly three moves :D
Samthere
CC BY-SA 3.0
2017-08-08T13:39:36.583Z
@freekvd Every move I label as "forced" is one which, if black _doesn't_ take that move, black loses immediately.
Samthere
CC BY-SA 3.0
2016-02-02T11:18:26.997Z
2016-02-02T15:49:55.780Z
2016-02-02T15:49:55.780Z
Samthere
<p>In this <a href="http://www.logicmazes.com/games/epam/index.html" rel="noreferrer">description of Epaminondas with puzzles at the bottom</a>, what is the solution to the first puzzle?</p>

<p><a href="https://i.sstatic.net/5dOpc.png" rel="noreferrer"><img src="https://i.sstatic.net/5dOpc.png" alt="enter image description here"></a></p>

<puzzles><epaminondas>
Epaminondas puzzle
hkBst
# Epaminondas puzzle

(Asked by: username_0 on 2016-02-02)

In this [description of Epaminondas with puzzles at the bottom](http://www.logicmazes.com/games/epam/index.html), what is the solution to the first puzzle?

[![enter image description here](https://i.sstatic.net/5dOpc.png)](https://i.sstatic.net/5dOpc.png)

**Tags:** puzzles, epaminondas


---

## 1 answers

### Answer by username_1 on 2016-02-02. Score: 3

The solution is for white to move their row of 3 one space forward. There are a bunch of possible moves for black but white can guarantee a win from all of them.

[![enter image description here](https://i.sstatic.net/mna1g.png)](https://i.sstatic.net/mna1g.png)

# If black moves away from their back line:

If black moves their leftmost piece away from the line, then red pushes forward. Black is forced to use their remaining 2 to capture red, who captures again. Black can't capture the remaining piece.

[![enter image description here](https://i.sstatic.net/SwqjM.png)](https://i.sstatic.net/SwqjM.png)

This is similar to the situation with the rightmost piece:

[![enter image description here](https://i.sstatic.net/LzLpb.png)](https://i.sstatic.net/LzLpb.png)

If black moves the middle piece away, then they will have to reform the broken 2 in order to defend the back line. Red aims a phalanx there:

[![enter image description here](https://i.sstatic.net/7oCbM.png)](https://i.sstatic.net/7oCbM.png)

If black moves the middle piece to the side to avoid this diagonal phalanx, red goes too far away on the other side:

[![enter image description here](https://i.sstatic.net/lDi3B.png)](https://i.sstatic.net/lDi3B.png)

# If black stays on the back line

If black is staying on the back line, then their first move cannot be to the left. Any distance to the left allows red to take the first capture and keep pushing to win. Thus black moves right. If black moves more than one space to the right, then they're too far away to defend from the single piece moving in. If black moves one space to the right, red forces the black row to capture their piece, lining up the black phalanx to be split in half:

[![enter image description here](https://i.sstatic.net/UoNe5.png)](https://i.sstatic.net/UoNe5.png)

> **Comments:**
> **username_1**: That said, this question is probably more suited to the [Puzzling Stack Exchange](http://puzzling.stackexchange.com).  
> **username_1**: And probably this answer is oversimplified - I've been playing with having black make the best defensive move each time and it's tough!  
> **username_0**: You cannot choose how black moves; you should show that it cannot play in any way so as to prevent the win by white. Also to win white only needs one of its pieces on black's back rank (since black is nowhere near white's back rank).  
> **username_1**: @username_0 Right! I think I've got it, just working through the possibilities.  
> **username_1**: @username_0 Okay, I worked it out over lunch with some board game parts :P I'll write it up now!  
> **username_2**: From [the help](http://boardgames.stackexchange.com/help/on-topic): "Questions about Go problems or Chess problems are fine, even if they are static puzzles, since they are related to a dynamic game." Can be extended to Epaminondas so this question is certainly on-topic here (as well as on Puzzling).  
> **username_1**: NOPE I GOT IT WRONG AGAIN AAAAAAAAAAAAAAAAAAAAAAAAAAARGH  
> **username_1**: Okay, I've actually got it! Finishing this up.  
> **username_2**: I don't think these 'forced captures' are mandatory, sorry.  
> **username_0**: If the middle black piece moves out of line, red can immediately move forwards for a win, because black cannot recapture.  
> **username_1**: @username_0 Right you are, but I this way gets a win in exactly three moves :D  
> **username_1**: @username_2 Every move I label as "forced" is one which, if black _doesn't_ take that move, black loses immediately.  

---

