Pêche à la ligne
10 71 32 23 14 15 16 27 18 19
20 81 72 53 44 35
26 47 38 29
40 101 82 73 64
65 56 77 58 39
60 131 92 93 74 75 86 107 88 69
80 201 122
113 84 85 96 117 138 89
La ligne 1 doit se lire :
« La ligne 1 comporte un "zéro" (1 0), sept "un" (7 1), trois "deux" (3 2), deux "trois" (2 3), etc. »
La ligne 2 se lit :
« L'ensemble formé par les lignes 1 et 2 comporte deux "zéro" (2 0), huit "un" (8 1), sept "deux" (7 2), etc.
La ligne 3 se lit :
« L'ensemble formé par les lignes 1, 2 et 3, comporte quatre "zéro" (4 0), dix "un" (10 1), huit "deux" (8 2), etc.
Le dernier nombre de la dernière ligne (89) se lit : « Il y a, dans ce tableau de 5 lignes, huit "neuf" en tout ».
On voit qu'à chaque étape il s'agit d'ajouter un décompte complet des chiffres présents dans le tableau correspondant.
Pour vérifier le total des chiffres "3" par exemple, j'ai copié/collé le tableau complet dans Word et remplacé tous les "3" par des "3" ; Word m'a affiché le nombre de substitutions effectuées par lui – ce qui m'a donné le compte cherché (ici 11 car il y a bien onze "3" dans le tableau, d'où le 113 de la dernière ligne).
Update of March 14th, 15th now, 2020
Gilles Esposito-Farèse has suggested that a 6-line array is impossible, whatever the start (the 1st line could have been 10 111 22 13 14 15 16 17 18 19).
Lars Blomberg confirms that a 6-row array is impossible – but he found a second solution for the 5-lines array:
10, 71, 32, 23, 14, 15, 16, 27, 18, 19. (same 1st line as above) 20, 81, 72, 53, 44, 35, 26, 47, 38, 29. (same 2nd line as above) 30, 111, 82, 83, 74, 45, 46, 77, 68, 39. (new lines by Lars from here on) 40, 151, 92, 93, 94, 75, 56, 117, 78, 79. 60, 241, 112, 113, 114, 85, 76, 137, 108, 89.
Meantime, Gilles built a 53-line array in base 2:
11 0, 100 1.
1001 0, 1000 1.
10000 0, 1100 1.
10101 0, 10011 1.
11001 0, 11011 1.
11110 0, 100011 1.
100101 0, 101010 1.
101011 0, 110010 1.
110001 0, 111010 1.
111010 0, 1000000 1.
111111 0, 1001010 1.
1001001 0, 1010000 1.
1001111 0, 1011010 1.
1011000 0, 1100001 1.
1100001 0, 1101000 1.
1100111 0, 1110010 1.
1101100 0, 1111101 1.
1110011 0, 10000111 1.
1111011 0, 10010000 1.
1111111 0, 10011101 1.
10001001 0, 10100101 1.
10010001 0, 10101111 1.
10010111 0, 10111011 1.
10100001 0, 11000011 1.
10101010 0, 11001100 1.
10110001 0, 11010111 1.
10111001 0, 11100001 1.
10111110 0, 11101110 1.
11000101 0, 11111001 1.
11001111 0, 100000010 1.
11010111 0, 100001101 1.
11011111 0, 100011000 1.
11101001 0, 100100001 1.
11101111 0, 100101110 1.
11110110 0, 100111010 1.
11111101 0, 101000110 1.
100001000 0, 101001111 1.
100010011 0, 101011000 1.
100011101 0, 101100010 1.
100100110 0, 101101101 1.
100101110 0, 101111001 1.
100111001 0, 110000010 1.
101000100 0, 110001011 1.
101001101 0, 110010110 1.
101010111 0, 110100000 1.
101011110 0, 110101101 1.
101100110 0, 110111001 1.
101101110 0, 111000101 1.
101110110 0, 111010001 1.
110000000 0, 111011011 1.
110001001 0, 111100110 1.
110010010 0, 111110001 1.
110011000 0, 111111111 1.
There is another 53-line aray, found Gilles – 35th line (yellow) and below:
11 0, 100 1.
1001 0, 1000 1.
10000 0, 1100 1.
10101 0, 10011 1.
11001 0, 11011 1.
11110 0, 100011 1.
100101 0, 101010 1.
101011 0, 110010 1.
110001 0, 111010 1.
111010 0, 1000000 1.
111111 0, 1001010 1.
1001001 0, 1010000 1.
1001111 0, 1011010 1.
1011000 0, 1100001 1.
1100001 0, 1101000 1.
1100111 0, 1110010 1.
1101100 0, 1111101 1.
1110011 0, 10000111 1.
1111011 0, 10010000 1.
1111111 0, 10011101 1.
10001001 0, 10100101 1.
10010001 0, 10101111 1.
10010111 0, 10111011 1.
10100001 0, 11000011 1.
10101010 0, 11001100 1.
10110001 0, 11010111 1.
10111001 0, 11100001 1.
10111110 0, 11101110 1.
11000101 0, 11111001 1.
11001111 0, 100000010 1.
11010111 0, 100001101 1.
11011111 0, 100011000 1.
11101001 0, 100100001 1.
11101111 0, 100101110 1.
11111000 0, 100111000 1.
11111111 0, 101000100 1.
100001010 0, 101001101 1.
100010100 0, 101010111 1.
100011110 0, 101100001 1.
100100111 0, 101101100 1.
100101111 0, 101111000 1.
100111010 0, 110000001 1.
101000101 0, 110001010 1.
101010000 0, 110010011 1.
101011000 0, 110011111 1.
101011111 0, 110101100 1.
101100111 0, 110111000 1.
101101111 0, 111000100 1.
101110111 0, 111010000 1.
110000001 0, 111011010 1.
110001010 0, 111100101 1.
110010011 0, 111110000 1.
110011001 0, 111111110 1.
On voit qu'à chaque étape il s'agit d'ajouter un décompte complet des chiffres présents dans le tableau correspondant.
Pour vérifier le total des chiffres "3" par exemple, j'ai copié/collé le tableau complet dans Word et remplacé tous les "3" par des "3" ; Word m'a affiché le nombre de substitutions effectuées par lui – ce qui m'a donné le compte cherché (ici 11 car il y a bien onze "3" dans le tableau, d'où le 113 de la dernière ligne).
Gilles Esposito-Farèse has suggested that a 6-line array is impossible, whatever the start (the 1st line could have been 10 111 22 13 14 15 16 17 18 19).
Lars Blomberg confirms that a 6-row array is impossible – but he found a second solution for the 5-lines array:
10, 71, 32, 23, 14, 15, 16, 27, 18, 19. (same 1st line as above) 20, 81, 72, 53, 44, 35, 26, 47, 38, 29. (same 2nd line as above) 30, 111, 82, 83, 74, 45, 46, 77, 68, 39. (new lines by Lars from here on) 40, 151, 92, 93, 94, 75, 56, 117, 78, 79. 60, 241, 112, 113, 114, 85, 76, 137, 108, 89.
Meantime, Gilles built a 53-line array in base 2:
11 0, 100 1.
1001 0, 1000 1.
10000 0, 1100 1.
10101 0, 10011 1.
11001 0, 11011 1.
11110 0, 100011 1.
100101 0, 101010 1.
101011 0, 110010 1.
110001 0, 111010 1.
111010 0, 1000000 1.
111111 0, 1001010 1.
1001001 0, 1010000 1.
1001111 0, 1011010 1.
1011000 0, 1100001 1.
1100001 0, 1101000 1.
1100111 0, 1110010 1.
1101100 0, 1111101 1.
1110011 0, 10000111 1.
1111011 0, 10010000 1.
1111111 0, 10011101 1.
10001001 0, 10100101 1.
10010001 0, 10101111 1.
10010111 0, 10111011 1.
10100001 0, 11000011 1.
10101010 0, 11001100 1.
10110001 0, 11010111 1.
10111001 0, 11100001 1.
10111110 0, 11101110 1.
11000101 0, 11111001 1.
11001111 0, 100000010 1.
11010111 0, 100001101 1.
11011111 0, 100011000 1.
11101001 0, 100100001 1.
11101111 0, 100101110 1.
11110110 0, 100111010 1.
11111101 0, 101000110 1.
100001000 0, 101001111 1.
100010011 0, 101011000 1.
100011101 0, 101100010 1.
100100110 0, 101101101 1.
100101110 0, 101111001 1.
100111001 0, 110000010 1.
101000100 0, 110001011 1.
101001101 0, 110010110 1.
101010111 0, 110100000 1.
101011110 0, 110101101 1.
101100110 0, 110111001 1.
101101110 0, 111000101 1.
101110110 0, 111010001 1.
110000000 0, 111011011 1.
110001001 0, 111100110 1.
110010010 0, 111110001 1.
110011000 0, 111111111 1.
There is another 53-line aray, found Gilles – 35th line (yellow) and below:
11 0, 100 1.
1001 0, 1000 1.
10000 0, 1100 1.
10101 0, 10011 1.
11001 0, 11011 1.
11110 0, 100011 1.
100101 0, 101010 1.
101011 0, 110010 1.
110001 0, 111010 1.
111010 0, 1000000 1.
111111 0, 1001010 1.
1001001 0, 1010000 1.
1001111 0, 1011010 1.
1011000 0, 1100001 1.
1100001 0, 1101000 1.
1100111 0, 1110010 1.
1101100 0, 1111101 1.
1110011 0, 10000111 1.
1111011 0, 10010000 1.
1111111 0, 10011101 1.
10001001 0, 10100101 1.
10010001 0, 10101111 1.
10010111 0, 10111011 1.
10100001 0, 11000011 1.
10101010 0, 11001100 1.
10110001 0, 11010111 1.
10111001 0, 11100001 1.
10111110 0, 11101110 1.
11000101 0, 11111001 1.
11001111 0, 100000010 1.
11010111 0, 100001101 1.
11011111 0, 100011000 1.
11101001 0, 100100001 1.
11101111 0, 100101110 1.
11111000 0, 100111000 1.
11111111 0, 101000100 1.
100001010 0, 101001101 1.
100010100 0, 101010111 1.
100011110 0, 101100001 1.
100100111 0, 101101100 1.
100101111 0, 101111000 1.
100111010 0, 110000001 1.
101000101 0, 110001010 1.
101010000 0, 110010011 1.
101011000 0, 110011111 1.
101011111 0, 110101100 1.
101100111 0, 110111000 1.
101101111 0, 111000100 1.
101110111 0, 111010000 1.
110000001 0, 111011010 1.
110001010 0, 111100101 1.
110010011 0, 111110000 1.
110011001 0, 111111110 1.
We have also those arrays (by Gilles):
11 lines in base 3:
1 0, 11 1, 2 2.
11 0, 101 1, 10 2.
20 0, 112 1, 21 2.
110 0, 200 1, 100 2.
112 0, 220 1, 111 2.
121 0, 1011 1, 122 2.
201 0, 1022 1, 212 2.
212 0, 1112 1, 1000 2.
221 0, 1211 1, 1011 2.
1011 0, 2000 1, 1022 2.
1022 0, 2020 1, 1111 2.
26 lines in base 4:
1 0, 11 1, 2 2, 1 3.
10 0, 21 1, 10 2, 3 3.
11 0, 32 1, 13 2, 12 3.
13 0, 102 1, 23 2, 21 3.
22 0, 112 1, 100 2, 23 3.
23 0, 122 1, 112 2, 32 3.
31 0, 133 1, 122 2, 102 3.
33 0, 210 1, 132 2, 112 3.
110 0, 220 1, 203 2, 120 3.
120 0, 230 1, 213 2, 130 3.
123 0, 233 1, 230 2, 201 3.
133 0, 302 1, 300 2, 212 3.
203 0, 311 1, 303 2, 230 3.
211 0, 322 1, 313 2, 301 3.
213 0, 331 1, 323 2, 320 3.
230 0, 1000 1, 331 2, 333 3.
301 0, 1012 1, 333 2, 1010 3.
313 0, 1031 1, 1001 2, 1020 3.
322 0, 1111 1, 1012 2, 1023 3.
1000 0, 1123 1, 1022 2, 1033 3.
1011 0, 1203 1, 1032 2, 1102 3.
1021 0, 1231 1, 1102 2, 1110 3.
1031 0, 1313 1, 1110 2, 1120 3.
1102 0, 2000 1, 1121 2, 1121 3.
1111 0, 2022 1, 1131 2, 1130 3.
1122 0, 2033 1, 1203 2, 1200 3.
... the last two lines above can be changed into:
1112 0, 2020 1, 1132 2, 1130 3.
1122 0, 2100 1, 1210 2, 1132 3.
2 lines in base 5 (no more?!):
1 0, 11 1, 2 2, 1 3, 1 4.
3 0, 14 1, 3 2, 10 3, 3 4.
2 lines in base 6:
1 0, 11 1, 2 2, 1 3, 1 4, 1 5.
2 0, 13 1, 4 2, 5 3, 3 4, 3 5.
2 lines in base 7:
1 0, 11 1, 2 2, 1 3, 1 4, 1 5, 1 6.
2 0, 13 1, 5 2, 4 3, 4 4, 3 5, 2 6.
5 lines in base 8:
1 0, 11 1, 2 2, 1 3, 1 4, 1 5, 1 6, 1 7.
2 0, 13 1, 6 2, 4 3, 4 4, 2 5, 3 6, 2 7.
3 0, 15 1, 7 2, 6 3, 5 4, 7 5, 5 6, 5 7.
7 0, 23 1, 11 2, 10 3, 6 4, 10 5, 7 6, 10 7.
12 0, 34 1, 15 2, 12 3, 10 4, 12 5, 10 6, 11 7.
5 lines in base 9:
1 0, 6 1, 3 2, 2 3, 1 4, 1 5, 2 6, 1 7, 1 8.
2 0, 7 1, 6 2, 5 3, 4 4, 3 5, 4 6, 3 7, 2 8.
4 0, 10 1, 7 2, 6 3, 8 4, 4 5, 7 6, 6 7, 4 8.
6 0, 15 1, 8 2, 7 3, 10 4, 6 5, 11 6, 8 7, 8 8.
8 0, 26 1, 12 2, 10 3, 11 4, 7 5, 13 6, 11 7, 11 8.
5 lines in base 10:
1 0, 7 1, 3 2, 2 3, 1 4, 1 5, 1 6, 2 7, 1 8, 1 9.
2 0, 8 1, 7 2, 5 3, 4 4, 3 5, 2 6, 4 7, 3 8, 2 9.
4 0, 10 1, 8 2, 7 3, 6 4, 6 5, 5 6, 7 7, 5 8, 3 9.
6 0, 13 1, 9 2, 9 3, 7 4, 7 5, 8 6, 10 7, 8 8, 6 9.
8 0, 20 1, 12 2, 11 3, 8 4, 8 5, 9 6, 11 7, 13 8, 8 9.
3 lines in base 11:
1 0, 8 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 2 8, 1 9, 1 A.
2 0, 9 1, 8 2, 6 3, 3 4, 2 5, 3 6, 2 7, 4 8, 3 9, 2 A.
4 0, 10 1, 9 2, 8 3, 7 4, 4 5, 6 6, 4 7, 6 8, 5 9, 3 A.
3 lines in base 12:
1 0, 9 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 2 9, 1 A, 1 B.
2 0, A 1, 9 2, 6 3, 3 4, 2 5, 3 6, 2 7, 2 8, 4 9, 3 A, 2 B.
4 0, 10 1, A 2, 8 3, 7 4, 6 5, 5 6, 4 7, 4 8, 5 9, 5 A, 3 B.
3 lines in base 13:
1 0, A 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 2 A, 1 B, 1 C.
2 0, B 1, A 2, 6 3, 3 4, 2 5, 3 6, 2 7, 2 8, 2 9, 4 A, 3 B, 2 C.
4 0, 10 1, B 2, 9 3, 7 4, 6 5, 5 6, 4 7, 3 8, 4 9, 5 A, 5 B, 3 C.
5 lines in base 14:
8 lines in base 15:
1 0, C 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 1 A, 1 B, 2 C, 1 D, 1 E.
2 0, D 1, C 2, 5 3, 4 4, 3 5, 2 6, 2 7, 2 8, 2 9, 2 A, 2 B, 4 C, 3 D, 2 E.
3 0, 11 1, D 2, B 3, 8 4, 6 5, 4 6, 3 7, 4 8, 3 9, 3 A, 4 B, 5 C, 5 D, 3 E.
4 0, 13 1, E 2, D 3, B 4, A 5, 8 6, 5 7, 6 8, 4 9, 5 A, 6 B, 6 C, 7 D, 5 E.
6 0, 16 1, 10 2, E 3, C 4, B 5, C 6, 8 7, A 8, 6 9, 7 A, 8 B, 9 C, 8 D, 7 E.
8 0, 1A 1, 12 2, 10 3, D 4, C 5, D 6, 9 7, D 8, 9 9, A A, B B, B C, D D, 8 E.
9 0, 21 1, 15 2, 11 3, E 4, E 5, E 6, A 7, E 8, B 9, C A, D B, D C, 12 D, D E.
D 0, 2E 1, 17 2, 13 3, 10 4, 11 5, 10 6, C 7, 10 8, C 9, D A, E B, 11 C, 15 D, 11 E.
1 0, 11 1, 2 2.
11 0, 101 1, 10 2.
20 0, 112 1, 21 2.
110 0, 200 1, 100 2.
112 0, 220 1, 111 2.
121 0, 1011 1, 122 2.
201 0, 1022 1, 212 2.
212 0, 1112 1, 1000 2.
221 0, 1211 1, 1011 2.
1011 0, 2000 1, 1022 2.
1022 0, 2020 1, 1111 2.
26 lines in base 4:
1 0, 11 1, 2 2, 1 3.
10 0, 21 1, 10 2, 3 3.
11 0, 32 1, 13 2, 12 3.
13 0, 102 1, 23 2, 21 3.
22 0, 112 1, 100 2, 23 3.
23 0, 122 1, 112 2, 32 3.
31 0, 133 1, 122 2, 102 3.
33 0, 210 1, 132 2, 112 3.
110 0, 220 1, 203 2, 120 3.
120 0, 230 1, 213 2, 130 3.
123 0, 233 1, 230 2, 201 3.
133 0, 302 1, 300 2, 212 3.
203 0, 311 1, 303 2, 230 3.
211 0, 322 1, 313 2, 301 3.
213 0, 331 1, 323 2, 320 3.
230 0, 1000 1, 331 2, 333 3.
301 0, 1012 1, 333 2, 1010 3.
313 0, 1031 1, 1001 2, 1020 3.
322 0, 1111 1, 1012 2, 1023 3.
1000 0, 1123 1, 1022 2, 1033 3.
1011 0, 1203 1, 1032 2, 1102 3.
1021 0, 1231 1, 1102 2, 1110 3.
1031 0, 1313 1, 1110 2, 1120 3.
1102 0, 2000 1, 1121 2, 1121 3.
1111 0, 2022 1, 1131 2, 1130 3.
1122 0, 2033 1, 1203 2, 1200 3.
... the last two lines above can be changed into:
1112 0, 2020 1, 1132 2, 1130 3.
1122 0, 2100 1, 1210 2, 1132 3.
2 lines in base 5 (no more?!):
1 0, 11 1, 2 2, 1 3, 1 4.
3 0, 14 1, 3 2, 10 3, 3 4.
2 lines in base 6:
1 0, 11 1, 2 2, 1 3, 1 4, 1 5.
2 0, 13 1, 4 2, 5 3, 3 4, 3 5.
2 lines in base 7:
1 0, 11 1, 2 2, 1 3, 1 4, 1 5, 1 6.
2 0, 13 1, 5 2, 4 3, 4 4, 3 5, 2 6.
5 lines in base 8:
1 0, 11 1, 2 2, 1 3, 1 4, 1 5, 1 6, 1 7.
2 0, 13 1, 6 2, 4 3, 4 4, 2 5, 3 6, 2 7.
3 0, 15 1, 7 2, 6 3, 5 4, 7 5, 5 6, 5 7.
7 0, 23 1, 11 2, 10 3, 6 4, 10 5, 7 6, 10 7.
12 0, 34 1, 15 2, 12 3, 10 4, 12 5, 10 6, 11 7.
5 lines in base 9:
1 0, 6 1, 3 2, 2 3, 1 4, 1 5, 2 6, 1 7, 1 8.
2 0, 7 1, 6 2, 5 3, 4 4, 3 5, 4 6, 3 7, 2 8.
4 0, 10 1, 7 2, 6 3, 8 4, 4 5, 7 6, 6 7, 4 8.
6 0, 15 1, 8 2, 7 3, 10 4, 6 5, 11 6, 8 7, 8 8.
8 0, 26 1, 12 2, 10 3, 11 4, 7 5, 13 6, 11 7, 11 8.
5 lines in base 10:
1 0, 7 1, 3 2, 2 3, 1 4, 1 5, 1 6, 2 7, 1 8, 1 9.
2 0, 8 1, 7 2, 5 3, 4 4, 3 5, 2 6, 4 7, 3 8, 2 9.
4 0, 10 1, 8 2, 7 3, 6 4, 6 5, 5 6, 7 7, 5 8, 3 9.
6 0, 13 1, 9 2, 9 3, 7 4, 7 5, 8 6, 10 7, 8 8, 6 9.
8 0, 20 1, 12 2, 11 3, 8 4, 8 5, 9 6, 11 7, 13 8, 8 9.
3 lines in base 11:
1 0, 8 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 2 8, 1 9, 1 A.
2 0, 9 1, 8 2, 6 3, 3 4, 2 5, 3 6, 2 7, 4 8, 3 9, 2 A.
4 0, 10 1, 9 2, 8 3, 7 4, 4 5, 6 6, 4 7, 6 8, 5 9, 3 A.
3 lines in base 12:
1 0, 9 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 2 9, 1 A, 1 B.
2 0, A 1, 9 2, 6 3, 3 4, 2 5, 3 6, 2 7, 2 8, 4 9, 3 A, 2 B.
4 0, 10 1, A 2, 8 3, 7 4, 6 5, 5 6, 4 7, 4 8, 5 9, 5 A, 3 B.
3 lines in base 13:
1 0, A 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 2 A, 1 B, 1 C.
2 0, B 1, A 2, 6 3, 3 4, 2 5, 3 6, 2 7, 2 8, 2 9, 4 A, 3 B, 2 C.
4 0, 10 1, B 2, 9 3, 7 4, 6 5, 5 6, 4 7, 3 8, 4 9, 5 A, 5 B, 3 C.
5 lines in base 14:
1 0, B 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 1 A, 2 B, 1 C, 1 D.
2 0, C 1, B 2, 6 3, 3 4, 2 5, 3 6, 2 7, 2 8, 2 9, 2 A, 4 B, 3 C, 2 D.
3 0, D 1, C 2, A 3, 7 4, 6 5, 5 6, 4 7, 3 8, 3 9, 4 A, 5 B, 5 C, 4 D.
5 0, 12 1, 10 2, B 3, 9 4, 9 5, A 6, 6 7, 4 8, 6 9, 6 A, 7 B, 6 C, 5 D.
6 0, 16 1, 11 2, C 3, A 4, A 5, D 6, 8 7, 9 8, 8 9, A A, 8 B, 8 C, 7 D.
... with another possible last line:
6 0, 16 1, 11 2, C 3, A 4, A 5, D 6, 9 7, 7 8, 9 9, A A, 8 B, 8 C, 7 D.
8 lines in base 15:
1 0, C 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 1 A, 1 B, 2 C, 1 D, 1 E.
2 0, D 1, C 2, 5 3, 4 4, 3 5, 2 6, 2 7, 2 8, 2 9, 2 A, 2 B, 4 C, 3 D, 2 E.
3 0, 11 1, D 2, B 3, 8 4, 6 5, 4 6, 3 7, 4 8, 3 9, 3 A, 4 B, 5 C, 5 D, 3 E.
4 0, 13 1, E 2, D 3, B 4, A 5, 8 6, 5 7, 6 8, 4 9, 5 A, 6 B, 6 C, 7 D, 5 E.
6 0, 16 1, 10 2, E 3, C 4, B 5, C 6, 8 7, A 8, 6 9, 7 A, 8 B, 9 C, 8 D, 7 E.
8 0, 1A 1, 12 2, 10 3, D 4, C 5, D 6, 9 7, D 8, 9 9, A A, B B, B C, D D, 8 E.
9 0, 21 1, 15 2, 11 3, E 4, E 5, E 6, A 7, E 8, B 9, C A, D B, D C, 12 D, D E.
D 0, 2E 1, 17 2, 13 3, 10 4, 11 5, 10 6, C 7, 10 8, C 9, D A, E B, 11 C, 15 D, 11 E.
10 lines in base 16:
1 0, D 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 1 A, 1 B, 1 C, 2 D, 1 E, 1 F.
2 0, E 1, D 2, 5 3, 4 4, 3 5, 2 6, 2 7, 2 8, 2 9, 2 A, 2 B, 2 C, 4 D, 3 E, 2 F.
3 0, 11 1, E 2, C 3, 8 4, 6 5, 4 6, 3 7, 4 8, 3 9, 3 A, 3 B, 4 C, 5 D, 5 E, 3 F.
4 0, 13 1, F 2, E 3, C 4, A 5, 7 6, 7 7, 5 8, 4 9, 5 A, 4 B, 6 C, 6 D, 7 E, 5 F.
6 0, 16 1, 10 2, F 3, D 4, B 5, C 6, A 7, 9 8, 6 9, 7 A, 6 B, 8 C, 8 D, 8 E, 7 F.
8 0, 1A 1, 12 2, 10 3, E 4, C 5, D 6, B 7, C 8, 9 9, B A, 9 B, C C, A D, A E, 8 F.
B 0, 21 1, 14 2, 11 3, 10 4, D 5, E 6, C 7, D 8, B 9, C A, C B, 10 C, E D, D E, 9 F.
C 0, 2A 1, 19 2, 12 3, 11 4, E 5, F 6, D 7, E 8, D 9, E A, E B, 12 C, 11 D, 12 E, B F.
E 0, 33 1, 1C 2, 16 3, 13 4, F 5, 12 6, E 7, F 8, E 9, F A, F B, 14 C, 12 D, 16 E, 10 F.
12 0, 43 1, 1F 2, 1B 3, 15 4, 12 5, 13 6, 10 7, 10 8, F 9, 10 A, 11 B, 15 C, 13 D, 17 E, 13 F.
...with the last line having another possibility:
12 0, 43 1, 21 2, 1A 3, 15 4, 12 5, 13 6, 10 7, 10 8, F 9, 11 A, 10 B, 15 C, 13 D, 17 E, 12 F.
1 0, x 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 1 a, 1 b, 1 c, 1 d, 1 e, 1 f, 1 g, 1 h, 1 i, 1 j, 1 k, 1 l, 1 m, 1 n, 1 o, 1 p, 1 q, 1 r, 1 s, 1 t, 1 u, 1 v, 1 w, 2 x, 1 y, 1 z
2 0, y 1, x 2, 6 3, 3 4, 2 5, 3 6, 2 7, 2 8, 2 9, 2 a, 2 b, 2 c, 2 d, 2 e, 2 f, 2 g, 2 h, 2 i, 2 j, 2 k, 2 l, 2 m, 2 n, 2 o, 2 p, 2 q, 2 r, 2 s, 2 t, 2 u, 2 v, 2 w, 4 x, 3 y, 2 z
3 0, z 1, y 2, w 3, 7 4, 6 5, 5 6, 4 7, 3 8, 3 9, 3 a, 3 b, 3 c, 3 d, 3 e, 3 f, 3 g, 3 h, 3 i, 3 j, 3 k, 3 l, 3 m, 3 n, 3 o, 3 p, 3 q, 3 r, 3 s, 3 t, 3 u, 3 v, 4 w, 5 x, 5 y, 4 z
5 0, 12 1, 10 2, x 3, t 4, d 5, 8 6, 6 7, 5 8, 4 9, 4 a, 4 b, 4 c, 5 d, 4 e, 4 f, 4 g, 4 h, 4 i, 4 j, 4 k, 4 l, 4 m, 4 n, 4 o, 4 p, 4 q, 4 r, 4 s, 5 t, 4 u, 4 v, 5 w, 7 x, 6 y, 5 z
6 0, 16 1, 11 2, y 3, u 4, w 5, h 6, 8 7, 9 8, 6 9, 5 a, 5 b, 5 c, 6 d, 5 e, 5 f, 5 g, 6 h, 5 i, 5 j, 5 k, 5 l, 5 m, 5 n, 5 o, 5 p, 5 q, 5 r, 5 s, 6 t, 6 u, 5 v, 7 w, 8 x, 8 y, 6 z
Merci Gilles et Lars — et bravo !
(This idea was shown in the wonderful Futility Closet of Sharon and Greg, here)
And to end as we started (in French), look at this wonderful task by Gilles, computed in a few minutes! (I have great, clever and kind friends!-)
1 0, D 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 1 A, 1 B, 1 C, 2 D, 1 E, 1 F.
2 0, E 1, D 2, 5 3, 4 4, 3 5, 2 6, 2 7, 2 8, 2 9, 2 A, 2 B, 2 C, 4 D, 3 E, 2 F.
3 0, 11 1, E 2, C 3, 8 4, 6 5, 4 6, 3 7, 4 8, 3 9, 3 A, 3 B, 4 C, 5 D, 5 E, 3 F.
4 0, 13 1, F 2, E 3, C 4, A 5, 7 6, 7 7, 5 8, 4 9, 5 A, 4 B, 6 C, 6 D, 7 E, 5 F.
6 0, 16 1, 10 2, F 3, D 4, B 5, C 6, A 7, 9 8, 6 9, 7 A, 6 B, 8 C, 8 D, 8 E, 7 F.
8 0, 1A 1, 12 2, 10 3, E 4, C 5, D 6, B 7, C 8, 9 9, B A, 9 B, C C, A D, A E, 8 F.
B 0, 21 1, 14 2, 11 3, 10 4, D 5, E 6, C 7, D 8, B 9, C A, C B, 10 C, E D, D E, 9 F.
C 0, 2A 1, 19 2, 12 3, 11 4, E 5, F 6, D 7, E 8, D 9, E A, E B, 12 C, 11 D, 12 E, B F.
E 0, 33 1, 1C 2, 16 3, 13 4, F 5, 12 6, E 7, F 8, E 9, F A, F B, 14 C, 12 D, 16 E, 10 F.
12 0, 43 1, 1F 2, 1B 3, 15 4, 12 5, 13 6, 10 7, 10 8, F 9, 10 A, 11 B, 15 C, 13 D, 17 E, 13 F.
...with the last line having another possibility:
12 0, 43 1, 21 2, 1A 3, 15 4, 12 5, 13 6, 10 7, 10 8, F 9, 11 A, 10 B, 15 C, 13 D, 17 E, 12 F.
and a 5-line array in base 36 (no capitalized letters to distinguish o/0 and i/1:
1 0, x 1, 3 2, 2 3, 1 4, 1 5, 1 6, 1 7, 1 8, 1 9, 1 a, 1 b, 1 c, 1 d, 1 e, 1 f, 1 g, 1 h, 1 i, 1 j, 1 k, 1 l, 1 m, 1 n, 1 o, 1 p, 1 q, 1 r, 1 s, 1 t, 1 u, 1 v, 1 w, 2 x, 1 y, 1 z
2 0, y 1, x 2, 6 3, 3 4, 2 5, 3 6, 2 7, 2 8, 2 9, 2 a, 2 b, 2 c, 2 d, 2 e, 2 f, 2 g, 2 h, 2 i, 2 j, 2 k, 2 l, 2 m, 2 n, 2 o, 2 p, 2 q, 2 r, 2 s, 2 t, 2 u, 2 v, 2 w, 4 x, 3 y, 2 z
3 0, z 1, y 2, w 3, 7 4, 6 5, 5 6, 4 7, 3 8, 3 9, 3 a, 3 b, 3 c, 3 d, 3 e, 3 f, 3 g, 3 h, 3 i, 3 j, 3 k, 3 l, 3 m, 3 n, 3 o, 3 p, 3 q, 3 r, 3 s, 3 t, 3 u, 3 v, 4 w, 5 x, 5 y, 4 z
5 0, 12 1, 10 2, x 3, t 4, d 5, 8 6, 6 7, 5 8, 4 9, 4 a, 4 b, 4 c, 5 d, 4 e, 4 f, 4 g, 4 h, 4 i, 4 j, 4 k, 4 l, 4 m, 4 n, 4 o, 4 p, 4 q, 4 r, 4 s, 5 t, 4 u, 4 v, 5 w, 7 x, 6 y, 5 z
6 0, 16 1, 11 2, y 3, u 4, w 5, h 6, 8 7, 9 8, 6 9, 5 a, 5 b, 5 c, 6 d, 5 e, 5 f, 5 g, 6 h, 5 i, 5 j, 5 k, 5 l, 5 m, 5 n, 5 o, 5 p, 5 q, 5 r, 5 s, 6 t, 6 u, 5 v, 7 w, 8 x, 8 y, 6 z
Merci Gilles et Lars — et bravo !
(This idea was shown in the wonderful Futility Closet of Sharon and Greg, here)
And to end as we started (in French), look at this wonderful task by Gilles, computed in a few minutes! (I have great, clever and kind friends!-)
Cette première phrase compte six a, un b, cinq c, cinq d,
dix-neuf e, deux f, un g, quatre h, quatorze i, un j, un k, un l, trois m,
treize n, quatre o, six p, huit q, dix r, sept s, quinze t, dix-huit u, un v,
un w, sept x, un y et quatre z.
Ces deux premières phrases comptent ensemble quinze a, trois
b, dix c, quatorze d, cinquante-six e, quatre f, quatre g, sept h, trente et un
i, deux j, deux k, trois l, sept m, trente n, onze o, treize p, dix-sept q,
vingt-six r, vingt et un s, quarante-trois t, trente-cinq u, quatre v, deux w, dix-huit
x, deux y et neuf z.
Ces trois premières phrases comptent en tout vingt-sept
a, quatre b, quinze c, vingt et un d, quatre-vingt-six e, six f, dix g, onze h,
soixante i, trois j, trois k, quatre l, dix m, cinquante-deux n, vingt-trois o,
dix-huit p, vingt-six q, quarante-quatre r, trente-huit s, soixante-dix-neuf t,
cinquante et un u, dix v, trois w, trente x, trois y et treize z.
Ces quatre premières phrases comptent en tout quarante-trois
a, cinq b, vingt-cinq c, vingt-sept d, cent vingt-six e, huit f, dix-huit g,
seize h, quatre-vingt-sept i, quatre j, quatre k, cinq l, treize m,
quatre-vingts n, trente et un o, vingt-cinq p, quarante et un q, soixante-deux
r, cinquante-trois s, cent vingt-deux t, soixante et onze u, dix-huit v, quatre
w, trente-neuf x, quatre y et dix-sept z.
Ces cinq premières phrases comptent au total soixante a, six
b, trente-neuf c, trente et un d, cent soixante-neuf e, treize f, vingt-trois
g, dix-neuf h, cent seize i, cinq j, cinq k, sept l, seize m, cent quatorze n,
quarante-cinq o, trente et un p, cinquante-quatre q, soixante-dix-neuf r, soixante-douze
s, cent soixante-trois t, quatre-vingt-sept u, vingt-trois v, cinq w,
quarante-huit x, cinq y et vingt-trois z.
Ces six phrases totalisent soixante-dix-neuf a, sept b, cinquante-deux
c, quarante d, deux cent quinze e, dix-sept f, trente g, vingt-quatre h, cent
quarante-cinq i, six j, six k, onze l, dix-huit m, cent cinquante et un n,
cinquante-huit o, trente-neuf p, soixante-sept q, quatre-vingt-quatorze r, quatre-vingt-dix
s, deux cent sept t, cent douze u, vingt-neuf v, six w, soixante-quatre x, six
y et vingt-huit z, et l'on pourrait continuer encore longtemps...
____________________
Bonjour les gars, contactez deadlyhacker01@gmail.com ou WhatsApp: +1 3478577580 si vous avez besoin d'embaucher un vrai pirate pour surveiller à distance le téléphone portable de votre conjoint.
RépondreSupprimer