---
id: 5900f4601000cf542c50ff72
title: 'Problem 244: Sliders'
challengeType: 5
forumTopicId: 301891
dashedName: problem-244-sliders
---
# --description--
You probably know the game Fifteen Puzzle. Here, instead of numbered tiles, we have seven red tiles and eight blue tiles.
A move is denoted by the uppercase initial of the direction (Left, Right, Up, Down) in which the tile is slid, e.g. starting from configuration ($S$), by the sequence $LULUR$ we reach the configuration ($E$):
($S$) 
, ($E$) 
For each path, its checksum is calculated by (pseudocode):
$$\begin{align}
& \text{checksum} = 0 \\\\
& \text{checksum} = (\text{checksum} × 243 + m_1) \\; \text{mod} \\; 100\\,000\\,007 \\\\
& \text{checksum} = (\text{checksum} × 243 + m_2) \\; \text{mod} \\; 100\\,000\\,007 \\\\
& \ldots \\\\
& \text{checksum} = (\text{checksum} × 243 + m_n) \\; \text{mod} \\; 100\\,000\\,007
\end{align}$$
where $m_k$ is the ASCII value of the $k^{\text{th}}$ letter in the move sequence and the ASCII values for the moves are:
$$\begin{array}{|c|c|}
\hline
L & 76 \\\\ \hline
R & 82 \\\\ \hline
U & 85 \\\\ \hline
D & 68 \\\\ \hline
\end{array}$$
For the sequence $LULUR$ given above, the checksum would be 19761398. Now, starting from configuration ($S$), find all shortest ways to reach configuration ($T$).
($S$) 
, ($T$) 
What is the sum of all checksums for the paths having the minimal length?
# --hints--
`sliders()` should return `96356848`.
```js
assert.strictEqual(sliders(), 96356848);
```
# --seed--
## --seed-contents--
```js
function sliders() {
return true;
}
sliders();
```
# --solutions--
```js
// solution required
```