生於 1974
巧計零至百
1/9 * 7/4 * 0/4 * 2/3 | = | 0 | 1/9 * 7/4 * 0/4 | = | 0 | 1 * 9 - 7 - sqrt(4) | = | 0 | ||
1^974 + 0^423 | = | 1 | 1^974 - 0^4 | = | 1 | -1 - 9 + 7 + 4 | = | 1 | ||
1 * 9 * 7 * 4 * 0 + (4 + 2)/3 | = | 2 | 1^(9 * 7) + 4^(0 * 4) | = | 2 | 1/(9 - 7) * 4 | = | 2 | ||
1 * 9/(7-4) + 0 * 4/(2-3) | = | 3 | 1 + 9 - 7 + 4 + 0 - 4 | = | 3 | 1 * 9/(7 - 4) | = | 3 | ||
-1 + sqrt(9) - 7 + sqrt(4) - 0 + sqrt(4) + 2 + 3 | = | 4 | 1 + 9/(7 - 4) + 0/4 | = | 4 | 1^(9 - 7) * 4 | = | 4 | ||
(1 + 9 + 7 + 4 + 0 + 4)/(2 + 3) | = | 5 | (1 * 9 + 7 + 4)/(0 + 4) | = | 5 | 1 + (9 + 7)/4 | = | 5 | ||
(((1 * 9 + 7)/4 - 0) * 4 + 2)/3 | = | 6 | (1 + 9)P(7 - 4)/(0! + 4)! | = | 6 | sqrt(1 * 9 + 7) + sqrt(4) | = | 6 | ||
19 * 7 - 4 * 0 - 42 * 3 | = | 7 | (1 + 9 - 7)! + (4 + 0)/4 | = | 7 | 1 + 9 - 7 + 4 | = | 7 | ||
1^(9 * 7) + 4 + 0^(4 * 2) + 3 | = | 8 | 1 * 9 + 7 - 4 - 0 - 4 | = | 8 | 1 * (9 - 7) * 4 | = | 8 | ||
(1 + 9 + 7 + 4 + 0 + 4 + 2)/3 | = | 9 | 1^9 + 7 + (4 + 0)/4 | = | 9 | 1 * sqrt(9) * (7 - 4) | = | 9 | ||
(1 + 9) * (7 - 4) - (0 + 4)*(2 + 3) | = | 10 | 1 * 9 - 7 + 4 + 0 + 4 | = | 10 | (-1)^9 + 7 + 4 | = | 10 | ||
(((1 + 9) * 7 + 4) * 0 + 4)* 2 + 3 | = | 11 | 1 + 9 - 7 + 4 - 0 + 4 | = | 11 | 1^9 * (7 + 4) | = | 11 | ||
1 + 9 - 7 + 4 - 0 + 4 - 2 + 3 | = | 12 | 1^9 * (7 - 4) * (0 + 4) | = | 12 | 1 * 9 + 7 - 4 | = | 12 | ||
1 * (9 - 7)^4 + 0^(4 - 2) - 3 | = | 13 | 1^9 + 7 + 4^0 + 4 | = | 13 | 1 + 9 + 7 - 4 | = | 13 | ||
1^97 + 4 + 0 + 4 + 2 + 3 | = | 14 | 1 + 9 + 74 * 0 + 4 | = | 14 | 1^9 * 7 * sqrt(4) | = | 14 | ||
1 * 9 + 7 * 4 * 0 * 4 + 2 * 3 | = | 15 | -1 + 9 + 7 + 4 * 0 * 4 | = | 15 | 1 + sqrt(9) + 7 + 4 | = | 15 | ||
1 + 9 + 7 - 4 + 0 + 4 + 2 - 3 | = | 16 | (1 + 9 * 7)/(4 + 0 * 4) | = | 16 | (1 + 9 * 7)/4 | = | 16 | ||
1^9 + 7 + 4 + 0^4 + 2 + 3 | = | 17 | 1 * sqrt(9) + 7 * sqrt(4) + 0 * sqrt(4) | = | 17 | 1 + (9 - 7)^4 | = | 17 | ||
(1 + 9 - 7) * 4 + (0 + 4 - 2) * 3 | = | 18 | 1 * 9!/7! /(4 + 0 * 4) | = | 18 | 1 * 9!/7!/4 | = | 18 | ||
sqrt(1 * 9 + 7) * 4 + 0 + 4 + 2 - 3 | = | 19 | 1 + 9!/7!/(4 * 0 + 4) | = | 19 | 1 + 9 + 7 + sqrt(4) | = | 19 | ||
1 + (9 - 7) * (4 - 0) * (4 - 2) + 3 | = | 20 | 1 * 9 + 7 + 4 * 0 + 4 | = | 20 | 1 - 9 + 7 * 4 | = | 20 | ||
(1 + 9)!/7!/4!/0! - 4 - 2 - 3 | = | 21 | 1 + 9 + 7 + 4 + 0^4 | = | 21 | 1 + 9 + 7 + 4 | = | 21 | ||
1!! + 9!!/7!! + 4!! + 0!! + 4!! - 2!! - 3!! | = | 22 | (1 + 9) * (7 + 4)/(0! + 4) | = | 22 | 19 + 7 - 4 | = | 22 | ||
1 * sqrt(9) + 7 * sqrt(4) + 0 * sqrt(4) + 2 * 3 | = | 23 | 1 * 9 * (7 - 4) - 0 - 4 | = | 23 | (-1)^97 + 4! | = | 23 | ||
1^9 + 7 + 4 + 0 + 4 + 2^3 | = | 24 | (1 + 9 - 7) * (4 - 0 + 4) | = | 24 | (1 + 9 - 7) * 4!! | = | 24 | ||
1 + 9 + 7 + 4 + (0 - 4) * (2 - 3) | = | 25 | 1 + 9 + 7 + 4 + 0 + 4 | = | 25 | 1 + ((9 + 7)/4)! | = | 25 | ||
1 * 9 + 7 + 4 * 0 + 4 + 2 * 3 | = | 26 | (1 + 9)!/7!/4! - 0 - 4 | = | 26 | -1 + 9 * (7 - 4) | = | 26 | ||
(1 + 9 - 7 + 4 * 0 * 4)^2 * 3 | = | 27 | 1 * 9 * (7 - 4) - 0 * 4 | = | 27 | 1 * sqrt(9)^(7 - 4) | = | 27 | ||
1 * (9 - 7) * 4 + (0 + 4) * (2 + 3) | = | 28 | 1 + sqrt(9)^(7 - 4) - 0 * 4 | = | 28 | 1^9 * 7 * 4 | = | 28 | ||
1 * 9 + 7 * 4 - 0^4 - 2^3 | = | 29 | 1^9 + 7 * 4 + 0^4 | = | 29 | 1^9 + 7 + 4 | = | 29 | ||
1 + 9 + 7 + 4 + 0 + 4 + 2 + 3 | = | 30 | (1 + 9)C(7 - 4)/(0 + 4) | = | 30 | (1 + 9)C7/4 | = | 30 | ||
1 * 9 + 7 * 4 - 0 * 4 - 2 * 3 | = | 31 | (1 + 9) * (7 - 4) + 0!^4 | = | 31 | -1 + 9C7 - 4 | = | 31 | ||
(1 + 9)!/(7! * 4!) + (0 + 4)!/(2! * 3!) | = | 32 | 1 * (9 - 7) * 4 * (0 + 4) | = | 32 | (1^9 + 7) * 4 | = | 32 | ||
1 * 9 * (7 - 4) + 0 * 4 + 2 * 3 | = | 33 | 1 - 9 - 7 + 4! + 0 + 4! | = | 33 | 1 * sqrt(9) * (7 + 4) | = | 33 | ||
(1 + 9) * (7 - 4) - (0 + 4) * (2 - 3) | = | 34 | (1 + 9) * (7 - 4) + 0 + 4 | = | 34 | (1 + 9 + 7) * sqrt(4) | = | 34 | ||
1 * 9 * 7 - 4 + 0 - 4 * 2 * 3 | = | 35 | (1 * 9)C7 - (4 + 0)C4 | = | 35 | 1 + sqrt(9) + 7 + 4! | = | 35 | ||
1 + 9 + 7 + 4 + 0 + 4P2 + 3 | = | 36 | 1 * 9C7 * 4C(0 + 4) | = | 36 | (1 + sqrt(9)) * (7 + sqrt(4)) | = | 36 | ||
1^9 + 7 * 4 - 0 * 4 + 2^3 | = | 37 | 1 * 9 + 7 * 4 + 0 * 4 | = | 37 | 1 + 9!!/7!! * 4 | = | 37 | ||
(1^9 + 7) * 4 + (0^4 + 2) * 3 | = | 38 | 1 + 9C7 + (4 + 0)/4 | = | 38 | 1 + 9 + 7 * 4 | = | 38 | ||
1^9 * 7 + 4 * 0 + 4 * 2^3 | = | 39 | 1 + 9 + 7 * 4 + 0!^4 | = | 39 | -1 + 9C7 + 4 | = | 39 | ||
1 * (9 + 7 + 4) * (0 + 4 + 2)/3 | = | 40 | (1 + sqrt(9)) * (7 - sqrt(4)) * (0 + sqrt(4)) | = | 40 | 1 + 9 * 7 - 4! | = | 40 | ||
1! * 9 * 7 - 4! + 0! * 4 * 2 - 3! | = | 41 | 1 + 9C7 * 4C0 + 4 | = | 41 | 1 + 9C7 + 4 | = | 41 | ||
1 * 9 * 7 * 4/(0 * 4 + 2 * 3) | = | 42 | 1 + 9C7 + 4C0 + 4 | = | 42 | 1 * sqrt(9) * 7 * sqrt(4) | = | 42 | ||
1 * 9 + 7 * 4 + 0 * 4 + 2 * 3 | = | 43 | 1 + sqrt(9) * 7 * sqrt(4) + 0 * sqrt(4) | = | 43 | 1 + sqrt(9) * 7 * sqrt(4) | = | 43 | ||
1^9 * (7 + 4) * (0 - 4) * (2 - 3) | = | 44 | 1^9 * (7 + 4) * (0 + 4) | = | 44 | (1 + sqrt(9) + 7) * 4 | = | 44 | ||
1 * 9C(7 - 4) - 0 - 42 + 3 | = | 45 | (1 + sqrt(9)) * (7 - sqrt(4)) + 0! + 4! | = | 45 | 1 + 9 +7C4 | = | 45 | ||
(1 + 9 - 7)! + (4 + 0)! + 4! - 2^3 | = | 46 | (-1 * 9 + 7) + sqrt(4) * (0 + 4)! | = | 46 | -1 * sqrt(9) + 7^sqrt(4) | = | 46 | ||
1 + 9C7 + 4C0 + 4C2 + 3 | = | 47 | 1 * 9!/7! - 4C0 - 4! | = | 47 | -1! + 9!/7! - 4! | = | 47 | ||
(19 - 7) * 4 + 0 * (4 - 23) | = | 48 | ((1 + 9 - 7) * 4 - 0) * 4 | = | 48 | (19 - 7) * 4 | = | 48 | ||
(1 + 9 - 7 + 4)^((0 + 4 + 2)/3) | = | 49 | 1 * 97 - 4! - 0 - 4! | = | 49 | 1 + (9 - 7) * 4! | = | 49 | ||
(1 + 9) * 7 - 4 * 0 - 4 * (2 + 3) | = | 50 | -19 + 74 - 4 - (0 * 4)! | = | 50 | 1^sqrt(9) + 7^sqrt(4) | = | 50 | ||
1 * 9 * (7 - 4 - 0) + 4 * 2 * 3 | = | 51 | 1! + (9 - 7)! + (4 - 0)! + 4! | = | 51 | 1 * sqrt(9) * (-7 + 4!) | = | 51 | ||
1 + (9 - 7) * (4 + 0) * (4 + 2) + 3 | = | 52 | (1 + 9 + 7 - 4) * (0 + 4) | = | 52 | (1 * sqrt(9)! + 7) * 4 | = | 52 | ||
1! + 9C7 + 4C0 + 4C2 + 3! | = | 53 | 1 * 9 + (7 + 4) * (0 + 4) | = | 53 | (1 + sqrt(9)!) * 7 + 4 | = | 53 | ||
1! * 9!/7! - 4! + 0! * 4!/2! - 3! | = | 54 | 1 * 9 * 7 - 4 - 0! - 4 | = | 54 | 1 * 9 * (7 - 4)! | = | 54 | ||
(1 + 9) * (7 + 4) * (0 + 4)/2^3 | = | 55 | 19 + 7 + 4 + 0! + 4! | = | 55 | 1 + 9 * (7 - 4)! | = | 55 | ||
1 * 9 * 7 - 4 + 0 * 4 * 2 - 3 | = | 56 | 1 * 9C7 + 4 * (0! + 4) | = | 56 | (-1 + 9) * sqrt(7)^sqrt(4) | = | 56 | ||
19 + 7 + 4 + 0 + 4 + 23 | = | 57 | (1 + 9) * 7 - 4!! - 0! - 4! | = | 57 | (1 * 9 + 7!!)/sqrt(4) | = | 57 | ||
(1 + 9) * (7 + 4)/(0 + 4 - 2) + 3 | = | 58 | (-1 + 9) * 7 + 4 + sqrt(0) - sqrt(4) | = | 58 | 1 * 9 + 7^sqrt(4) | = | 58 | ||
1 + 9 + (7 + 4) * (0 + 4) + 2 + 3 | = | 59 | (1 + 9 + 7) * 4 - 0!! - 4!! | = | 59 | 1 + 9 +7^sqrt(4) | = | 59 | ||
1! + (9 - 7)! + 4! + 0! + 4! + 2! + 3! | = | 60 | (1 + 9) * (7 - (4 + 0)/4) | = | 60 | (1 + 9) * (7 - 4)! | = | 60 | ||
1 + 9 + 74 - 0 * 4 - 23 | = | 61 | 1 * 9 * 7 - 4!!/(0 + 4) | = | 61 | -1 + sqrt(9)! + 7 * 4!! | = | 61 | ||
(1 + 9 - 7)! + 4! + (0 + 4)! + 2! + 3! | = | 62 | (1 + 9) * 7 - 4 - 0 - 4 | = | 62 | (1 + 9) * 7 - 4!! | = | 62 | ||
1 + 97 + 4 + 0 - 42 + 3 | = | 63 | (1 * 9 * 7 * 4)/(0 + 4) | = | 63 | 1 * 9 * sqrt(7)^sqrt(4) | = | 63 | ||
(1 * 9 + 7) * 4 + 0 * (4 + 2 * 3) | = | 64 | 1 * 9 * 7 + 4^(0 * 4) | = | 64 | (1^9 + 7)^sqrt(4) | = | 64 | ||
(1 * 9 + 7) * (4 * 0 + 4) - 2 + 3 | = | 65 | (1 - sqrt(9) + 7) * (4!! + 0! + 4) | = | 65 | 1 + (9 + 7) * 4 | = | 65 | ||
19 + 74 - 0 - 4 - 23 | = | 66 | ((-1)^9 + 7) * (4!! - 0! + 4) | = | 66 | 1 - 9 + 74 | = | 66 | ||
19 + 7 + 4! + 0! + 4! - 2^3 | = | 67 | 1 * 9 * 7 + 4 * 0 + 4 | = | 67 | 1 * 9 * 7 + 4 | = | 67 | ||
(1 + 9 + 7) * 4 + 0 * (4 + 2 + 3) | = | 68 | 19 + 74 - 0! - 4! | = | 68 | (1 + 9 +7) * 4 | = | 68 | ||
1 * 9 * 7 + 4 * 0 * 4 + 2 * 3 | = | 69 | (1 + 9) * 7 - (4 + 0)/4 | = | 69 | -sqrt(1)! - sqrt(9)! + 74 | = | 69 | ||
19 + 7 * 4 + 0 * 4 + 23 | = | 70 | (1!! + 9!!/7!!) * (4 + 0! + 4) | = | 70 | (1 + 9) * sqrt(7)^sqrt(4) | = | 70 | ||
(1 + 9 + 7) * (4 + 0 + 4)/2 + 3 | = | 71 | 1 * 9C7 * sqrt(4) - 0!^4 | = | 71 | -1 + 9C7 * sqrt(4) | = | 71 | ||
1 * 9C7 * 4C0 * 4C2/3 | = | 72 | 1! + 9!/7! + 4! - 0! - 4! | = | 72 | 1!! * 9!!/7!! * 4!! | = | 72 | ||
(1 + 9 - 7)^4 - (0 + 4 - 2)^3 | = | 73 | (1 * 9)!/7! + (4 + 0)!/4! | = | 73 | 1 + 9C7 * sqrt(4) | = | 73 | ||
19 + 74 - 0 - 4 + 23 | = | 74 | 1^9 * 74 - 0^4 | = | 74 | (1 + 9) * 7 + 4 | = | 74 | ||
1 + 9 * 7 + 4 * 0 + 4 * 2 + 3 | = | 75 | 1^9 + 74 + 0^4 | = | 75 | 1^9 + 74 | = | 75 | ||
1 + 9C(7 - 4) - (0 + 4)C2 - 3 | = | 76 | (1 + 9) * 7 + 4!/(0 + 4) | = | 76 | 1 * 9!/7! + 4 | = | 76 | ||
1 * 9 * 7 + 4 * 0 + 4 * 2 + 3 | = | 77 | 19 + 7C4 - 0! + 4! | = | 77 | 1 + 9!/7! + 4 | = | 77 | ||
(1 + 9 + 7 + 4) * (0 + 4) - 2 * 3 | = | 78 | 1^9 * 74 + 0 + 4 | = | 78 | (1 + 9) * 7 + 4!! | = | 78 | ||
1 * 9!/7! + 4 + 0 * 4!/2! + 3 | = | 79 | -1!! + 9!!/7!! * 4!!/0!! + 4!! | = | 79 | -1 + (sqrt(9) + 7) * 4!! | = | 79 | ||
(1 + 9) * 7 + (4 + 0) * 4 - 2 * 3 | = | 80 | (1 + 9) * (7 + 4/(0 + 4)) | = | 80 | (1!! + 9!!/7!!) * 4!! | = | 80 | ||
(1 + 9 - 7)^4 + 0^(4 - 2 + 3) | = | 81 | (1 + 9 - 7)^(4 + 0 * 4) | = | 81 | (1 + 9 - 7)^4 | = | 81 | ||
(1 + 9) * 7 + 4 + 0^4 + 2^3 | = | 82 | (1 + 9) * 7 + 4!! + 0 + 4 | = | 82 | 1 + 9 * (7 + sqrt(4)) | = | 82 | ||
19 + 74 + 0! - 4 * 2 - 3 | = | 83 | 1 * 9 + 74 + 0 * 4 | = | 83 | 1 * 9 + 74 | = | 83 | ||
19 + 74 - 0 - 4 - 2 - 3 | = | 84 | (1 + 9 + 7 + 4) * (0 + 4) | = | 84 | 1 * 9C(7 - 4) | = | 84 | ||
19 + 74 - 0^4 - 2^3 | = | 85 | 1 + 9C(7 - 4) + 0 * 4 | = | 85 | 1 + 9C(7 - 4) | = | 85 | ||
(1 + 9 + 7) * 4 + (0 + 4 + 2) * 3 | = | 86 | (1 + 9) * 7 + (4 + 0) * 4 | = | 86 | -1! + sqrt(9)! + 7!! - 4! | = | 86 | ||
1 * 9 * 7 + 4 * 0 + 4 * 2 * 3 | = | 87 | 1! * 9 + 74 + 0! * 4 | = | 87 | 1 * 9 * 7 + 4! | = | 87 | ||
(1 + 9) * (7 +4) * (4 + 0)/(2 + 3) | = | 88 | 1 + 9 + 74 + 0 + 4 | = | 88 | (-1 + 9) * (7 + 4) | = | 88 | ||
(1 + 9 - 7)^4 + (0 + 4 - 2)^3 | = | 89 | 19 + 74 - 0 - 4 | = | 89 | 1 - 9 + 7!! - 4!! | = | 89 | ||
(1 + 9) * (7 + 4) - (0 + 4) * (2 + 3) | = | 90 | 1 * 9 * (7 + 4 - 0!^4) | = | 90 | (sqrt(1) + 9) * (7 + sqrt(4)) | = | 90 | ||
(1 + 9) * 7 + (4 + 0) * 4 + 2 + 3 | = | 91 | 1^9 * 7 * (4!! + 0! + 4) | = | 91 | -1 - 9 + 7!! - 4 | = | 91 | ||
1 + 9 * 7 + 4 + 0 + 4 * 2 * 3 | = | 92 | 19 + 74 - 0!^4 | = | 92 | -1 * 9 + 7!! - 4 | = | 92 | ||
1 + 97 + 40 - 42 - 3 | = | 93 | 19 + 74 + 0 * 4 | = | 93 | 19 + 74 | = | 93 | ||
1 + 9C(7 - 4) + (0 + 4)C2 + 3 | = | 94 | 1 + 97 - 4 - 0 * 4 | = | 94 | 1 + 97 - 4 | = | 94 | ||
1 + 9 + 74 + 0 + 4*2 + 3 | = | 95 | -1 + 97 - 4/(0 + 4) | = | 95 | 1 * 97 - sqrt(4) | = | 95 | ||
19 + 74 + 0 + 4 + 2 - 3 | = | 96 | (1 + 9)C7 - 4P(0 + 4) | = | 96 | (1 + 9)C7 - 4! | = | 96 | ||
(1!! + 9!!/7!!) * (4!! + 0!!) + 4!! + 2!! - 3!! | = | 97 | 19 + 74 + 0 + 4 | = | 97 | 1^9 * 7!! - 4!! | = | 97 | ||
1^9 + 74 + 0^4 + 23 | = | 98 | 1 * (9 - 7)! + 4 * (0 + 4)! | = | 98 | -1 + 9 * (7 + 4) | = | 98 | ||
19 + 74 + 0 * 4 + 2 * 3 | = | 99 | -1 + 9!/7! + 4!/0! + 4 | = | 99 | 1 * 9 * (7 + 4) | = | 99 | ||
(1 + 9)^(7 + 4 - 0 - 4 - 2 - 3) | = | 100 | (19 + 7) * 4 - 0 - 4 | = | 100 | -1 + 97 + 4 | = | 100 |
註:算式除了使用了加 (+)、減 (-)、乘 (*)、除 (/)、冪 (^)、括號以外,還使用了下列運算符號:
平方根 sqrt(x):如 sqrt(9) = 3 ,sqrt(1*9+7) = sqrt(16) = 4。
階乘 n! = n*(n-1)*(n-2)*...:如 5! = 120,3! = 6,0! = 1。
雙階乘 n!! = n*(n-2)*(n-4)*...:如 7!! = 105,4!! = 8,0!! = 1。
組合 nCr = n!/[(n-r)!r!]:如 9C7 = 36,4C0 = 1。
排列 nPr = n!/(n-r)!:如 9C(7-4) = 504,4P(0+4) = 24。
拼合:即把相鄰的兩個或多個數字看成一個兩位數或多位數,如把 1974 看成一個 4 位數。
創作巧計的過程
我生於一九七四年四月二十三日。看罷前輩的大作,蠢蠢欲動,望在二零一一年生日前後,利用生日數字作個宣傳小玩意。我是規定了數字的順序,原因是我想突顯生日日期,這也比不定字序難一些。原來創作過程不過數天,說難亦可,說易亦是,但總算總結了一些心得,供諸同好。
開始之時,我先擬定一些看來較美觀或對稱的算式,如:
1 + 9 + 7 + 4 + 0 + 4 + 2 + 3 = 30
1 * 9 + 7 * 4 + 0 * 4 + 2 * 3 = 43
1! + 9C7 + 4C0 + 4C2 + 3! = 53
19 + 7 + 4 + 0 + 4 + 23 = 57
1 * 9!/7! + 4 + 0 * 4!/2! + 3 = 79
這樣,我完成了約三十道算式。
其實起初希望只用四則和方冪而已,但漸漸感到有些算式弄不成,才增加運算符號而已。這兒我想,若減少運算方式,我可能要多想數天了。
接下來,我得看看各個數字的大能如何,如 9,可以是 9,可以是 sqrt(9) = 3,可以是 sqrt(9)! = 6等,又看看兩個數字或三個數字的組合有哪些可能性,再拼合出未完成的算式來。
完成八個數字以後,再向六個數字和四個數字挑戰,由於數字數目少了,也相應難了。說來八個數字的算式在二零一零年十二月左右完成,以期翌年生日發佈。而六個數字和四個數字則在二零一一年四月左右構思,五月十七日完成。那夜,我尚餘四個數字中的四道算式 (69 、75、86 和 89) 未許攻克,往慕道班的路途上,偶爾清風送爽,便找到了一些數值,算式便來了。這樣,我除了感謝神,還可說什麼呢。我苦思了數日也想不到的,一下了通了。
說回來計算還得仰仗我出生的日子不俗,當中有很多大大小小不同的數字,增加了數值的多樣性。更重要的是當中有一個進可攻,退可守的零:零可把多餘的數字「吃掉」,又可在加法中「自動消失」,必要時更可以化身 0!=1,充當一角。零這回真的可以說句:「別少看我耶」。
參考文獻及網址:
劉松基 "五秩進一" 自 數學中年漢的自述 , 香港 : 教育局課程發展處數學教育組 , p. 103-117 , 2010