---
id: 5900f4c81000cf542c50ffda
title: 'Problem 345: Matrix Sum'
challengeType: 1
forumTopicId: 302004
dashedName: problem-345-matrix-sum
---

# --description--

We define the Matrix Sum of a matrix as the maximum sum of matrix elements with each element being the only one in his row and column.

For example, the Matrix Sum of the matrix below equals $3315 ( = 863 + 383 + 343 + 959 + 767)$:

$$\begin{array}{rrrrr}
    7                &  53                & 183                & 439                & \color{lime}{863} \\\\
  497                & \color{lime}{383} & 563                &  79                & 973 \\\\
  287                &  63                & \color{lime}{343} & 169                & 583 \\\\
  627                & 343                & 773                & \color{lime}{959} & 943 \\\\
  \color{lime}{767} & 473                & 103                & 699                & 303
\end{array}$$

Find the Matrix Sum of:

$$\\begin{array}{r}
    7 &  53 & 183 & 439 & 863 & 497 & 383 & 563 &  79 & 973 & 287 &  63 & 343 & 169 & 583 \\\\
  627 & 343 & 773 & 959 & 943 & 767 & 473 & 103 & 699 & 303 & 957 & 703 & 583 & 639 & 913 \\\\
  447 & 283 & 463 &  29 &  23 & 487 & 463 & 993 & 119 & 883 & 327 & 493 & 423 & 159 & 743 \\\\
  217 & 623 &   3 & 399 & 853 & 407 & 103 & 983 &  89 & 463 & 290 & 516 & 212 & 462 & 350 \\\\
  960 & 376 & 682 & 962 & 300 & 780 & 486 & 502 & 912 & 800 & 250 & 346 & 172 & 812 & 350 \\\\
  870 & 456 & 192 & 162 & 593 & 473 & 915 &  45 & 989 & 873 & 823 & 965 & 425 & 329 & 803 \\\\
  973 & 965 & 905 & 919 & 133 & 673 & 665 & 235 & 509 & 613 & 673 & 815 & 165 & 992 & 326 \\\\
  322 & 148 & 972 & 962 & 286 & 255 & 941 & 541 & 265 & 323 & 925 & 281 & 601 &  95 & 973 \\\\
  445 & 721 &  11 & 525 & 473 &  65 & 511 & 164 & 138 & 672 &  18 & 428 & 154 & 448 & 848 \\\\
  414 & 456 & 310 & 312 & 798 & 104 & 566 & 520 & 302 & 248 & 694 & 976 & 430 & 392 & 198 \\\\
  184 & 829 & 373 & 181 & 631 & 101 & 969 & 613 & 840 & 740 & 778 & 458 & 284 & 760 & 390 \\\\
  821 & 461 & 843 & 513 &  17 & 901 & 711 & 993 & 293 & 157 & 274 &  94 & 192 & 156 & 574 \\\\
   34 & 124 &   4 & 878 & 450 & 476 & 712 & 914 & 838 & 669 & 875 & 299 & 823 & 329 & 699 \\\\
  815 & 559 & 813 & 459 & 522 & 788 & 168 & 586 & 966 & 232 & 308 & 833 & 251 & 631 & 107 \\\\
  813 & 883 & 451 & 509 & 615 &  77 & 281 & 613 & 459 & 205 & 380 & 274 & 302 &  35 & 805
\end{array}$$

# --hints--

`matrixSum()` should return `13938`.

```js
assert.strictEqual(matrixSum(), 13938);
```

# --seed--

## --seed-contents--

```js
function matrixSum() {

  return true;
}

matrixSum();
```

# --solutions--

```js
// solution required
```
