3 x 37 = 111 si 1 + 1 + 1 = 3
6 x 37 = 222 si 2 + 2 + 2 = 6
9 x 37 = 333 si 3 + 3 + 3 = 9
12 x 37 = 444 si 4 + 4 + 4 = 12
15 x 37 = 555 si 5 + 5 + 5 = 15
18 x 37 = 666 si 6 + 6 + 6 = 18
21 x 37 = 777 si 7 + 7 + 7 = 21
24 x 37 = 888 si 8 + 8 + 8 = 24
27 x 37 = 999 si 9 + 9 + 9 = 27 |
3 x 37 = 111 si 1 + 1 + 1 = 3
6 x 37 = 222 si 2 + 2 + 2 = 6
9 x 37 = 333 si 3 + 3 + 3 = 9
12 x 37 = 444 si 4 + 4 + 4 = 12
15 x 37 = 555 si 5 + 5 + 5 = 15
18 x 37 = 666 si 6 + 6 + 6 = 18
21 x 37 = 777 si 7 + 7 + 7 = 21
24 x 37 = 888 si 8 + 8 + 8 = 24
27 x 37 = 999 si 9 + 9 + 9 = 27 |
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321 |
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10 = 1111111111
|
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888 |
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321 |
7 x 7 = 49
67 x 67 = 4489
667 x 667 = 444889
6667 x 6667 = 44448889
66667 x 66667 = 4444488889
666667 x 666667 = 444444888889
6666667 x 6666667 = 44444448888889
etc |
4 x 4 = 16
34 x 34 = 1156
334 x 334 = 111556
3334 x 3334 = 11115556
33334 x 33334 = 1111155556
etc |
1 x 9 + 2 = 11
21 x 9 + 33 = 222
321 x 9 + 444 = 3 333
4 321 x 9 + 5 555 = 44 444
54 321 x 9 + 66 666 = 555 555
654 321 x 9 + 777 777 = 6 666 666
7 654 321 x 9 + 8 888 888 = 77 777 777
87 654 321 x 9 + 99 999 999 = 888 888 888
|
9 x 9 = 81
99 x 99 = 9 801
999 x 999 = 998 001
9 999 x 9 999 = 99 980 001
99 999 x 99 999 = 9 999 800 001
|
1 0013 = 1 003 003 001
2 0023 = 8 024 024 008
3 0033 = 27 081 081 027
4 0043 = 64 192 192 064
5 0053 = 125 375 375 125
6 0063 = 216 648 648 216
7 0073 = 344 030 029 343
8 0083 = 513 537 536 512
9 0093 = 731 189 187 729
|
32 + 192 + 222 = 62 + 172 + 232
34 + 194 + 224 = 64 + 174 + 234
36 + 196 + 226 = 106 + 156 + 236
92 + 6252 + 1 4442 = 492 + 4002 + 1 5212
91/2 + 6251/2 + 1 4441/2 = 491/2 + 4001/2 + 1 5211/2
51 + 12 + 66 = 35 + 74 + 20
512 + 122 + 662 = 352 + 742 + 202 |
De asemnenea putem scrie: |
Apoi : |
1 + 2 + 3 + ..... + 10 = 55
1 + 2 + 3 + ..... + 100 = 5 050
1 + 2 + 3 + ..... + 1000 = 500 500
................................
1 + 2 + 3 + ..... + 10k = 500...500...0 |
12 + 22 + 32 + ..... + 102 = 385
12 + 22 + 32 + ..... + 1002 = 338 350
12 + 222 + 32 + ..... + 10002 = 333 833 500
................................
12 + 22 + 32 + ..... + (10k)2 = 33...3833...3500...0 |
Puteri consecutive formate din aceleasi cifre : |
29 700 1572 = 882 099 325 824 649
29 700 158 2 = 882 099 385 224 964 |
