Expert: Josh - 11/12/2006

Question
Hello Josh,
I accidently reset my combination lock somehow (my laptop to a table), and now I don't know the sequence that opens it.  The lock is 3 numbers across, each with 0-9 on it.  What is the correct formula for figuring out the number of combinations of 3 numbers at a time that I can try to open it with? like most combo locks, the numbers can repeat, and the order does matter. And, please, maybe not as interesting to you, but even more helpful to me at this moment, is there a link to software or a chart, that I can print out the whole list so I can just cross them off as I try the combinations (without writing out the whole chart myself?). I love math, but I also need to free my shackled laptop as soon as possible.  Thank you! Michelle

Answer
Hi Michelle,

Are you sure you didn't write the number down somewhere? If you have got the initial code partially right, you may only have to crack, say, the last digit or something.

Unfortunately, following a brute-force approach, if you have absolutely no clue (even what prefix the code begins with), then, you will have to try all 10x10x10=1000 combinations in the worst case scenario.

If a professional locksmith, or a thief, has the patience and right skills, they may be able to unlock a mechanical device incrementally by listening to how the dial turns (see
http://home.howstuffworks.com/safecracking.htm). That is an art which few can master.

Digital safes are probably easier to manipulate (even if you have to try all different combinations). Unlocking a mechanical one would probably be very time-consuming.

Below is a list of all combinations. List A is in random order. If you have a digital safe and don't have a clue, then this is a reasonable strategy, as it is easy to punch in 3-digit numbers. Get someone to read it out to you. List B is ranked from smallest to largest. This is a systematic approach more suited to a mechanical safe where you have to turn the dial. This may take longer if you are unlucky, e.g., starting from the wrong end of scale.

Sorry, I cannot offer a faster solution, unless you can find a professional armed with the right tools.

List A: (Random order, concatenated)
979,725,656,806,239,824,727,770,888,940,
23,251,219, 91,533,154,632,525,688,795,
932,712,436,408,500,123, 30,732,161,679,
162,504,890,  7, 41,916,621,987,590,592,
152,900,359,898,875,627,158,566,207,823,
151,982,479,450,241,304,471,192,119,664,
842,329,882,165, 20,299,117,997,345,927,
488, 98,717,485,974,850,624,532,385,323,
469,540,531,887,193,462,567,684,313,170,
943,428,346,969,363,157,915,983,499,817,
484,660,763,724,903,587,815,405,552,335,
290,623,475,782,206,180,473,556,931,851,
708,761,498,456,849,905,144,620,907,910,
606,854, 90,220,598, 24,293,764,830,371,
605,666, 54,645,174,228,895,555,937,661,
637,917,212,977,355,874,869,896,838,227,
852,366,421,669,783,676,519,198,760,447,
84,197,388,655, 14,626,580,886,517,284,
929,920,380, 49,163,195,229,647,586,594,
792,686,541, 50,260,729,949,871, 26,247,
29,800, 93,470,341, 38,746, 25,145,976,
110,460,839,491,141,565,659,130,513,885,
840,762,857,972,440,908,768,105,534,445,
879,572,843,617,  1,775,190,788,187,939,
486,264,948,214,191,911,614,508,390,378,
596,454,829, 87,317,635,709,185,822,302,
412,622,928,510,950,489,211,137,836,856,
347, 86,563, 28,342,184,981,630,543,784,
767,411,716, 96,611,400,453,926,501,876,
482, 67,493,816,325,240, 94,777,813,431,
52, 48,121,404,964,846,528,398,689, 71,
835,906,526,845,668,153,897,774,545,202,
386,938,706,465,132,671,352,861,639,738,
692,819,103,602,267,980,327,201,569, 68,
396, 66,780,803,994,226,996,892,379, 21,
173,449,330,899,966,610,300,203,292,430,
166,257,631,933, 74,148,276,468,578,466,
477,365,250, 56, 43,542,867,651,111,737,
155,667,913,269,884,204,422,401,909,941,
272,818,609,674,246,397, 15,662,663,348,
382,984, 18,673,399,135,237,273,120,776,
35,564,252,582,321,230,101,364,277, 47,
222,310,104,332,603,128,810,200,138,652,
172,406,429,374,  9, 77, 32,427,687,758,
446,236,181,418,728,150,369,171,714,461,
 6,765,235,536,208,234,426,114,683,383,
393, 34,570,407, 97,745,604,416,349,718,
353,178,789,924,694,653,743,289,786,  3,
961,968,576,283,232,381,925, 60,331,129,
492,581, 45,548,402,755,739,675,392,539,
700,914,281,319,658,971,702,102,535,593,
423,599,442,474, 82,759,677, 37,790,108,
579,607, 69,837,629,344,520,394, 53,726,
772,954, 76,301,265,859,245,324,179,785,
435,507,695,721,713,464,333,781,740,588,
279,472,294,642,115, 73,425,262,636,305,
825,149,747,106,864,538,100,164,391,707,
771,205, 59,936,638,804,278,358,437,351,
354,303,480,883,316,514,118, 27,515,703,
 2,146,654,387,160,812,361,384,159,873,
10,805,696,334,698,855,731,375,258,389,
506, 79,904,521,248,343,613,270,143,756,
147,167,263,311,518,953,828,546,978,648,
377,616,109,194,678,963,131, 63,215,942,
243,831,559,841,722,773,274,268,992,574,
640,516,512, 65,583,965, 95,697,561,409,
291,217,619,497,748,844,711,957,649,340,
958, 39,778,494,584,970,296,801,175,749,
523,530,881,328,113, 42,618, 51,156,140,
699,522,225,169,809,242, 78,682, 55,934,
271,176,285,306,811,362,458, 75,537,288,
441,862,413, 46,922,858,444,951,701,946,
595,182,280,168,424,998,847,558,403,893,
410,973,868,608,134, 70,988,177,990,259,
320,249,628,672,224, 89,752, 13,309,993,
826,136, 31,866,308,511,253,560,337,451,
736,433,107,734,  5,557,496,741,796,124,
944,373,476,751,544,650,723,872,282,527,
742,947,112,414,730,766,889,127,657,338,
644, 11,757,791,901,254,116, 80,956,744,
312,710,681,419,188,287,827,360,553, 22,
798,339,833,233,438,502,985,962, 64,221,
505,959,685,  8, 62,509,705,295,478,550,
420,356, 44,646,367,691,680,275, 40, 72,
821,368,142,196,918,256, 36,459,989,955,
568,463,432,625, 58,231,814,326, 57,573,
641,186,634,753,467,612,209,372,591,218,
986,923,213,318,122,690, 88,524,891,919,
83,865,693,562,995,483,633,935,223,733,
575,  4,183, 19, 92,452,600,670,336,808,
61,238,417,261,715,735,554,189,769,350,
793,853,571,315, 17,930,551,255, 12,794,
720,799,529,802,912,834,266, 33,455,443,
487,139,597,210, 16,967,779,457,860,665,
395,601,750,863,820,314,832,797,549,481,
434,  0,878,376,787,848,991,357,870,370,
81,585,495,999,880,133,322,298,307,975,
704,216,894,448,589,945,960,125,877,439,
952,615, 85,643,807,286,244,719,503,415,
547, 99,126,754,921,577,199,902,297,490

List B:
 0,  1,  2,  3,  4,  5,  6,  7,  8,  9,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49,
50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
60, 61, 62, 63, 64, 65, 66, 67, 68, 69,
70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
90, 91, 92, 93, 94, 95, 96, 97, 98, 99,
100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,
120,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,
140,141,142,143,144,145,146,147,148,149,
150,151,152,153,154,155,156,157,158,159,
160,161,162,163,164,165,166,167,168,169,
170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,186,187,188,189,
190,191,192,193,194,195,196,197,198,199,
200,201,202,203,204,205,206,207,208,209,
210,211,212,213,214,215,216,217,218,219,
220,221,222,223,224,225,226,227,228,229,
230,231,232,233,234,235,236,237,238,239,
240,241,242,243,244,245,246,247,248,249,
250,251,252,253,254,255,256,257,258,259,
260,261,262,263,264,265,266,267,268,269,
270,271,272,273,274,275,276,277,278,279,
280,281,282,283,284,285,286,287,288,289,
290,291,292,293,294,295,296,297,298,299,
300,301,302,303,304,305,306,307,308,309,
310,311,312,313,314,315,316,317,318,319,
320,321,322,323,324,325,326,327,328,329,
330,331,332,333,334,335,336,337,338,339,
340,341,342,343,344,345,346,347,348,349,
350,351,352,353,354,355,356,357,358,359,
360,361,362,363,364,365,366,367,368,369,
370,371,372,373,374,375,376,377,378,379,
380,381,382,383,384,385,386,387,388,389,
390,391,392,393,394,395,396,397,398,399,
400,401,402,403,404,405,406,407,408,409,
410,411,412,413,414,415,416,417,418,419,
420,421,422,423,424,425,426,427,428,429,
430,431,432,433,434,435,436,437,438,439,
440,441,442,443,444,445,446,447,448,449,
450,451,452,453,454,455,456,457,458,459,
460,461,462,463,464,465,466,467,468,469,
470,471,472,473,474,475,476,477,478,479,
480,481,482,483,484,485,486,487,488,489,
490,491,492,493,494,495,496,497,498,499,
500,501,502,503,504,505,506,507,508,509,
510,511,512,513,514,515,516,517,518,519,
520,521,522,523,524,525,526,527,528,529,
530,531,532,533,534,535,536,537,538,539,
540,541,542,543,544,545,546,547,548,549,
550,551,552,553,554,555,556,557,558,559,
560,561,562,563,564,565,566,567,568,569,
570,571,572,573,574,575,576,577,578,579,
580,581,582,583,584,585,586,587,588,589,
590,591,592,593,594,595,596,597,598,599,
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,
700,701,702,703,704,705,706,707,708,709,
710,711,712,713,714,715,716,717,718,719,
720,721,722,723,724,725,726,727,728,729,
730,731,732,733,734,735,736,737,738,739,
740,741,742,743,744,745,746,747,748,749,
750,751,752,753,754,755,756,757,758,759,
760,761,762,763,764,765,766,767,768,769,
770,771,772,773,774,775,776,777,778,779,
780,781,782,783,784,785,786,787,788,789,
790,791,792,793,794,795,796,797,798,799,
800,801,802,803,804,805,806,807,808,809,
810,811,812,813,814,815,816,817,818,819,
820,821,822,823,824,825,826,827,828,829,
830,831,832,833,834,835,836,837,838,839,
840,841,842,843,844,845,846,847,848,849,
850,851,852,853,854,855,856,857,858,859,
860,861,862,863,864,865,866,867,868,869,
870,871,872,873,874,875,876,877,878,879,
880,881,882,883,884,885,886,887,888,889,
890,891,892,893,894,895,896,897,898,899,
900,901,902,903,904,905,906,907,908,909,
910,911,912,913,914,915,916,917,918,919,
920,921,922,923,924,925,926,927,928,929,
930,931,932,933,934,935,936,937,938,939,
940,941,942,943,944,945,946,947,948,949,
950,951,952,953,954,955,956,957,958,959,
960,961,962,963,964,965,966,967,968,969,
970,971,972,973,974,975,976,977,978,979,
980,981,982,983,984,985,986,987,988,989,
990,991,992,993,994,995,996,997,998,999