data/problems/345.yml
---
:id: 345
:name: Matrix Sum
:url: https://projecteuler.net/problem=345
:content: "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):\n\n 7
53 183 439 **863** \n497 **383** 563 79 973 \n287 63 **343**
169 583 \n627 343 773 **959** 943 \n**767** 473 103 699 303\n\nFind the Matrix
Sum of:\n\n 7 53 183 439 863 497 383 563 79 973 287 63
343 169 583 \n627 343 773 959 943 767 473 103 699 303 957 703 583 639 913 \n447
283 463 29 23 487 463 993 119 883 327 493 423 159 743 \n217 623 3
399 853 407 103 983 89 463 290 516 212 462 350 \n960 376 682 962 300 780
486 502 912 800 250 346 172 812 350 \n870 456 192 162 593 473 915 45 989
873 823 965 425 329 803 \n973 965 905 919 133 673 665 235 509 613 673 815 165 992
326 \n322 148 972 962 286 255 941 541 265 323 925 281 601 95 973 \n445 721
11 525 473 65 511 164 138 672 18 428 154 448 848 \n414 456 310
312 798 104 566 520 302 248 694 976 430 392 198 \n184 829 373 181 631 101 969 613
840 740 778 458 284 760 390 \n821 461 843 513 17 901 711 993 293 157 274
94 192 156 574 \n 34 124 4 878 450 476 712 914 838 669 875
299 823 329 699 \n815 559 813 459 522 788 168 586 966 232 308 833 251 631 107 \n813
883 451 509 615 77 281 613 459 205 380 274 302 35 805\n\n"