A three-digit numbers

Determine the total number of positive three-digit numbers that contain a digit 6.

Result

n =  252

Solution:

106, 116, 126, 136, 146, 156, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 176, 186, 196, 206, 216, 226, 236, 246, 256, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 276, 286, 296, 306, 316, 326, 336, 346, 356, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 376, 386, 396, 406, 416, 426, 436, 446, 456, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 476, 486, 496, 506, 516, 526, 536, 546, 556, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 576, 586, 596, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 706, 716, 726, 736, 746, 756, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 776, 786, 796, 806, 816, 826, 836, 846, 856, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 876, 886, 896, 906, 916, 926, 936, 946, 956, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 976, 986, 996
n= 252

$n = 10\cdot 10+9\cdot 10+9\cdot 10-10-10-9+1 = 252$

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