"Interstate 293 Interstate 293 (abbreviated I-293) is an long loop surrounding Manchester, New Hampshire, USA roughly shaped like two sides of a triangle. Completing the loop in the northeast (the third side of the triangle) is Interstate 93. The southern portion of the loop shares the road with NH 101 and passes near Manchester-Boston Regional Airport and the Mall of New Hampshire. The western portion of the loop shares the road with the Everett Turnpike, but there are no tolls on this portion of the turnpike. Interstate 293 begins at a directional T interchange in the southeast of Manchester, where"
"170, 182, 189, 201, 204, 214, 246, 285, 290, 361, 363, 386, 387, 394, 402, 479, 480, 483 (Luke corrector), 510, 511, 512, 516, 521, 547, 553, 558, 575, 586, 588, 594, 645, 660, 664, 673, 685, 689, 691, 694, 696, 757, 758, 763, 769, 781, 786, 789, 797, 802, 806, 824, 825, 845, 867, 897, 928, 932, 938, 940, 952, 953, 955, 959, 960, 962, 966, 973, 975, 1003, 1020, 1023, 1025, 1030, 1046, 1059, 1062, 1072, 1075, 1082, 1092, 1095, 1111, 1116, 1145, 1156, 1147, 1158, 1165, 1169, 1176, 1185, 1189, 1190, 1199, 1224, 1234, 1236, 1247, 1250,"
"462 463 464 465 466 467 468 469 470 471 472 473 475 476 477 478 479 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 542 543 544 545 546 547 548 549 550 551 552 553 554 556 557 558 559 560 562 563 564 567 568 569 570 571 572 573 574 575 580 588 590 591 599"
"seven jobs in destination zones. One configuration of such trips will be: where 0! = 1. That configuration can appear in 1,260 ways. We have calculated the number of ways that configuration of trips might have occurred, and to explain the calculation, let’s recall those coin tossing experiments talked about so much in elementary statistics. The number of ways a two-sided coin can come up is formula_26, where n is the number of times we toss the coin. If we toss the coin once, it can come up heads or tails, formula_27. If we toss it twice, it can come"
"or equal to 22 is 0 × 37 = 0. Subtracting 0 from 22 gives 22, we often don't write the subtraction step. Instead, we simply take another digit from the dividend: The process is repeated until 37 divides the last line exactly: For non-decimal currencies (such as the British £sd system before 1971) and measures (such as avoirdupois) mixed mode division must be used. Consider dividing 50 miles 600 yards into 37 pieces: Each of the four columns is worked in turn. Starting with the miles: 50/37 = 1 remainder 13. No further division is possible, so perform a"
"illustrated as follows. A marker is placed at zero on the number line, and a fair coin is flipped. If it lands on heads, the marker is moved one unit to the right. If it lands on tails, the marker is moved one unit to the left. After five flips, the marker could now be on 1, −1, 3, −3, 5, or −5. With five flips, three heads and two tails, in any order, it will land on 1. There are 10 ways of landing on 1 (by flipping three heads and two tails), 10 ways of landing on −1"
"Example: ""1234 − 567 ="" can be solved as follows: Subtraction Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtraction is signified by the minus sign (−). For example, in the adjacent picture, there are apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, the ""difference"" of 5 and 2 is 3, that is, . Subtraction represents removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions,"
"formula_17 could be defined to represent the state where there is one quarter, zero dimes, and five nickels on the table after 6 one-by-one draws. This new model would be represented by 216 possible states (that is, 6x6x6 states, since each of the three coin types could have zero to five coins on the table by the end of the 6 draws). Suppose that the first draw results in state formula_18. The probability of achieving formula_19 now depends on formula_20; for example, the state formula_21 is not possible. After the second draw, the third draw depends on which coins have"
"2282, 2426, 2437, 2445, 2459, 2490, 2491, 2507, 2536, 2549, 2550, 2552, 2562, 2639, 2650, 2657, 2671, 2700, 2712, 2725, 2727, 2781, 2785, 2791, 2794 <br> 632 and 1227 (composites of parts from the 12th to the 14th centuries) 905, 906, 1310, 1341, 1897, 2311 52, 55, 60, 74, 107, 121, 128, 136, 141, 147, 167, 170, 192, 198, 204, 219, 220, 227, 248, 260, 284, 291, 292, 293, 303, 305, 309, 327, 328, 342, 359, 361, 362, 384, 388, 390, 410, 449, 469, 473, 477, 479, 482, 483, 484, 496, 500, 501, 511, 519, 533, 534, 546, 553, 554,"
"can select: Straight (all four digits in exact order), Box (all four digits in any order), Straight/Box (all four digits), Pairs [two of the four digits in exact order, which can be: front pair (first two digits), middle pair (middle digits), or back pair (last two digits)], Combo [which can be: 4-way (three of the four digits drawn are identical, such as 1112), 6-way (the digits drawn are two pairs, such as 1122), 12-way (two of the four digits drawn are identical, such as 1123), or 24-way (all four digits are different, such as 1234)] and ""Sum It Up"" (see"
"Change-making problem The change-making problem addresses the question of finding the minimum number of coins (of certain denominations) that add up to a given amount of money. It is a special case of the integer knapsack problem, and has applications wider than just currency. It is also the most common variation of the ""coin change problem"", a general case of partition in which, given the available denominations of an infinite set of coins, the objective is to find out the number of possible ways of making a change for a specific amount of money, without considering the order of the"
"of getting any particular hexagram is the same in each method. However, the probabilities of getting old, changing lines are different. While in both methods there is a p = 4/16 = 1/4 chance of getting a changing line, in the coin method this is equally likely to be old yin or old yang (p = 2/16), whereas in the yarrow-stalk method, it is 200% more likely to be old yang than old yin (p = 3/16 compared to p = 1/16). The three coin method came into currency over a thousand years later. The quickest, easiest, and most popular"
"23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number. 383, prime number, safe prime, Woodall prime, Thabit number, Eisenstein prime with no imaginary part, palindromic prime. 385 = 5 × 7 × 11, sphenic number, square pyramidal number, the number of integer partitions of 18. 386 = 2 × 193, Nontotient, noncototient, centered heptagonal number, 386 is also shorthand for the Intel 80386 microprocessor chip. 386 generation refers to South Koreans, especially politicians, born in the '60s (). 387 = 3 × 43, also shorthand for the Intel 80387, math"
"number of three digits in base three, and positioning at the ""n""-th weighings all the coins that are labeled with the ""n""-th digit identical to the label of the plate (with three plates, one on each side of the scale and one off the scale). Other step-by-step procedures are similar to the following. It is less straightforward for this problem, and the second and third weighings depend on what has happened previously, although that need not be the case (see below). Given a population of 13 coins in which it is known that 1 of the 13 is different (mass)"
"111, 112, 113, 114, 115, 117, 118, 123, 124, 126, 127, 128, 129, 130, 132, 133, 134, 135, 136, 140, 141, 143, 146, 148, 150, 151, 152, 153, 154, 158, 159, 160, 161, 163, 165, 166, 168, 169, 172, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 188, 193, 194, 195. 200, 202, 203, 204, 205, 214, 215, 218, 219, 222, 228, 236, 237, 238, 239, 242, 243, 245, 247, 252, 253, 256, 257, 263, 264, 266, 269, 271, 273, 275, 276, 277, 278, 281, 283, 284, 288, 289, 291, 293, 295, 297, 298, 299, 300, 304,"
". Consider trying to compute , given , , and : One could use a calculator to compute 4; this comes out to 67,108,864. Taking this value modulo 497, the answer is determined to be 445. Note that is only one digit in length and that is only two digits in length, but the value is 8 digits in length. In strong cryptography, is often at least 1024 bits. Consider and , both of which are perfectly reasonable values. In this example, is 77 digits in length and is 2 digits in length, but the value is 1,304 decimal digits"
"multiply two numbers each up to 2-1. This scales very fast, so board with 20 numbers per side, for instance, can multiply numbers each up to a little over one million. Martin Gardner presented a slightly easier to understand version of Napier's division method, which is what is shown here. Division works pretty much the reverse of multiplication. Say we want to divide 485 by 13. First place counters for 485 (= 111100101) along the bottom edge and mark 13 (= 1101) along the right edge. To save space, we'll just look at a rectangular portion of the board because"
"coins. It is weakly NP-hard, but may be solved optimally in pseudo-polynomial time by dynamic programming. Coin values can be modeled by a set of distinct positive integer values (whole numbers), arranged in increasing order as through . The problem is: given an amount , also a positive integer, to find a set of non-negative (positive or zero) integers }, with each representing how often the coin with value is used, which minimize the total number of coins subject to An application of change-making problem can be found in computing the ways one can make a nine dart finish in"
"calculations. At least one triple machine was made. The Facit calculator, and one similar to it, are basically pinwheel machines, but the array of pinwheels moves sidewise, instead of the carriage. The pinwheels are biquinary; digits 1 through 4 cause the corresponding number of sliding pins to extend from the surface; digits 5 through 9 also extend a five-tooth sector as well as the same pins for 6 through 9. The keys operate cams that operate a swinging lever to first unlock the pin-positioning cam that is part of the pinwheel mechanism; further movement of the lever (by an amount"
"digits are different) averages $38. Unlike most lotteries, New Jersey pays winners of Pick-3 and Pick-4 on a parimutuel basis. Multiple wagers of the same number increase winnings. The most common Pick-3 wager is Straight and Box combined for $1.00 (sometimes known as a ""50-50"" bet.) Pick-4 is a four-digit draw game also drawn twice daily. It was introduced as a weekly game on July 9, 1977, became a daily game, and has been a twice-daily game since November 2001. The ways to win, in the order of payouts from highest to lowest, are: As in Pick-3, the most common"
"as long as ""s"" does not exceed ""m"". Otherwise, ""m"" is increased by 10 and some other digit is modified to correct for this increase. The American method corrects by attempting to decrease the minuend digit ""m"" by one (or continuing the borrow leftwards until there is a non-zero digit from which to borrow). The European method corrects by increasing the subtrahend digit ""s"" by one. Example: 704 − 512. The minuend is 704, the subtrahend is 512. The minuend digits are , and . The subtrahend digits are , and . Beginning at the one's place, 4 is not"
"1998, 2125, 2373, 2414, 2545, 2722, 2790 994, 1073, 1701 7p, 8, 12, 20, 23, 24, 25, 37, 39, 40, 50, 65, 68, 75, 77, 83, 89, 98, 108, 112, 123, 125, 126, 127, 133, 137, 142, 143, 148, 150, 177, 186, 194, 195, 197, 200, 207, 208, 210, 212, 215, 236, 250, 259, 272, 276, 277, 278a, 300, 301, 302, 314, 325, 331, 343, 350, 352, 354, 357, 360, 375, 376, 422, 458, 465, 466, 470, 474, 475, 476, 490, 491, 497, 504, 506, 507, 516, 526, 527, 528, 530, 532, 547, 548, 549, 560, 583, 585, 596, 607,"
"of the intermediate and outer edges is possible, including odd permutations, giving 24! arrangements for each set or 24! total, regardless of the position or orientation any other pieces. This gives a total number of permutations of The entire number is 19 500 551 183 731 307 835 329 126 754 019 748 794 904 992 692 043 434 567 152 132 912 323 232 706 135 469 180 065 278 712 755 853 360 682 328 551 719 137 311 299 993 600 000 000 000 000 000 000 000 000 000 000 000 (roughly 19,501 sexvigintillion or 19.5"
"129, 132, 134, 138, 139, 140, 146, 156, 159, 162, 183, 187, 193, 196, 199, 202, 203, 217, 224, 226, 231, 240, 244, 245, 247, 261, 264, 267, 268, 269, 270, 275, 280, 281, 282, 297, 304, 306, 319, 320, 329, 334, 337, 347, 351, 353, 355, 356, 366, 374, 387, 392, 395, 396, 401, 407, 408, 419, 438, 439, 443, 452, 471, 485, 499, 502, 505, 509, 510, 514, 518, 520, 524, 529, 531, 535, 538, 550, 551, 556, 570, 571, 580, 587, 618, 620, 622, 637, 650, 662, 673, 674, 688, 692, 721, 736, 748, 750, 760, 765,"
"which is the same column as the last digit of 111. The 111 is then subtracted from the line above, ignoring all digits to the right: Now the digit from the next smaller place value of the dividend is copied down appended to the result 15: The process repeats: the greatest multiple of 37 less than or equal to 150 is subtracted. This is 148 = 4 × 37, so a 4 is added to the solution line. Then the result of the subtraction is extended by another digit taken from the dividend: The greatest multiple of 37 less than"
"24! × 12! × 2 possibilities for the inner and outer edges together. This gives a total number of permutations of The full number is precisely 282 870 942 277 741 856 536 180 333 107 150 328 293 127 731 985 672 134 721 536 000 000 000 000 000 possible permutations (about 283 duodecillion on the long scale or 283 tresvigintillion on the short scale). Some variations of the Professor's Cube have one of the center pieces marked with a logo, which can be put into four different orientations. This increases the number of permutations by a factor"
"the remainder of division by eleven. This is called casting out elevens. Casting out nine hundred ninety nines is done by adding groups of three digits. Since 37·27 = 999, So we can use the remainder from casting out nine hundred ninety nines to get the remainder of division by thirty seven. Casting out nines The expression ""casting out nines"" may refer to any one of three arithmetical procedures: To ""cast out nines"" from a single number, its decimal digits can be simply added together to obtain its so-called digit sum. The digit sum of 2946, for example is 2"
"produce a room number: its digits will be [first digit of coach number]-[first digit of seat number]-[second digit of coach number]-[second digit of seat number]-etc. The hotel (coach #0) guest in room number 1729 moves to room 01070209 (i.e., room 1,070,209.) The passenger on seat 1234 of coach 789 goes to room 01728394 (or just 1728394). Unlike the prime powers solution, this one fills the hotel completely, and we can reconstruct a guest's original coach and seat by reversing the interleaving process. First add a leading zero if the room has an odd number of digits. Then de-interleave the number"
"However, in Director telephone areas such as the London telephone area, the changes permitted many new exchange codes to be issued that did not correspond to letters representing the geographic locations. As '1' was also available for the 'B' and 'C' digits, this allowed many more exchange codes such as 211, 219, 221 to be used. At the same time, many local exchange codes were altered in order to group them into geographic sectors (e.g. GROsvenor became 499 rather than 470) to eliminate the need for all incoming calls to be routed via central London. In the Director areas the"
"!align=""left"" colspan=3|Total !align=""right""|1,995 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|3,711 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|3,289 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|3,273 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|5,510 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,638 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|6,850 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|6,094 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,148 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,054 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|8,003 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,658 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,404 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|6,253 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|6,449 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,192 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,211 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,597 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|7,149 !align=""right""|100.00% !align=""right""| !align=""left"" colspan=3|Total !align=""right""|6,749 !align=""right""|100.00% !align=""right""|"
"1476 Working from right to left: Rule: Example: 346×4 = 1384 Working from right to left: Example: 42×5=210 Example: 357 × 6 = 2142 Working right to left, Rule: Example: 523 × 7 = 3,661. 3661. Rule: Example: 456 × 8 = 3648 Working from right to left: Rules: For rules 9, 8, 4, and 3 only the first digit is subtracted from 10. After that each digit is subtracted from nine instead. Example: 2,130 × 9 = 19,170 Working from right to left: Rule: Add the digit to its neighbor. (By ""neighbor"" we mean the digit on the right.)"
"put the 23 in the next column left. Now add up the three entries in the cwt column giving 587. This is 29 t 7 cwt, so write the 7 into the answer and the 29 in the column to the left. Now add up the tons column. There is no adjustment to make, so the result is just copied down. The same layout and methods can be used for any traditional measurements and non-decimal currencies such as the old British £sd system. Multiplication algorithm A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the"
"1093, 20771, 66161, 5, 1093, 11, 487, 71, 2693, 863, 29, 29131, 1093, 46021, 5, 7, 281, ?, 13, 13, 25633, 20771, 71, 11, 19, ?, 7, 7, 5, 233, 46145917691, 1613, 66161, 77867, 17, 8039, 11, 29, 23, 5, 229, 1283, 829, ?, 257, 491531, ?, ... (For ""k"" = 21, 29, 47, 50, even the next value is unknown) A Wieferich number is an odd natural number ""n"" satisfying the congruence 2 ≡ 1 (mod ""n""), where denotes the Euler's totient function (according to Euler's theorem, 2 ≡ 1 (mod ""n"") for every odd natural number ""n""). If"