terça-feira, 8 de março de 2011

Curiosidades com números inteiros

12345679 x  9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
12345679 x 72 = 888888888
12345679 x 81 = 999999999

9 x 9 + 7        = 88
9 x 98 + 6       = 888
9 x 987 + 5      = 8888
9 x 9876 + 4     = 88888
9 x 98765 + 3    = 888888
9 x 987654 + 2   = 8888888
9 x 9876543 + 1  = 88888888
9 x 98765432 + 0 = 888888888

9 x 1 + 2          = 11
9 x 12 + 3         = 111
9 x 123 + 4        = 1111
9 x 1234 + 5       = 11111
9 x 12345 + 6      = 111111
9 x 123456 + 7     = 1111111
9 x 1234567 + 8    = 11111111
9 x 12345678 + 9   = 111111111
9 x 123456789 + 10 = 1111111111

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

9        x 7        =        63
99       x 77       =       7623
999      x 777      =      776223
9999     x 7777     =     77762223
99999    x 77777    =    7777622223
999999   x 777777   =   777776222223
9999999  x 7777777  =  77777762222223
99999999 x 77777777 = 7777777622222223

1            x 7 + 3 = 10
14           x 7 + 2 = 100
142          x 7 + 6 = 1000
1428         x 7 + 4 = 10000
14285        x 7 + 5 = 100000
142857       x 7 + 1 = 1000000
1428571      x 7 + 3 = 10000000
14285714     x 7 + 2 = 100000000
142857142    x 7 + 6 = 1000000000
1428571428   x 7 + 4 = 10000000000
14285714285  x 7 + 5 = 100000000000
142857142857 x 7 + 1 = 1000000000000

9      x 9      =      81
99     x 99     =     9801
999    x 999    =    998001
9999   x 9999   =   99980001
99999  x 99999  =  9999800001
999999 x 999999 = 999998000001

12 x 12 =   144,  21 x 21 =   441
13 x 13 =   169,  31 x 31 =   961
102x102 = 10404,  201x201 = 40401
103x103 = 10609,  301x301 = 90601
112x112 = 12544,  211x211 = 44521
122x122 = 14884,  221x221 = 48841

99 = 9+8+7+65+4+3+2+1
100 = 1+2+3+4+5+6+7+8×9
134498697 = 1 + 2^3 + 4^5 + 6^7 + 8^9
1000 = 8 + 8 + 8 + 88 + 888

45 = 8+12+5+20,      8+2=12-2=5x2=20÷2=10
100 = 12+20+4+64,    12+4=20-4=4x4=64÷4=16
225 = 1+23+45+67+89, 89-67=67-45=45-23=23-1=22

5^2 + 2^1 = (5-2)^(2+1)
Notação: Para indicar que um número x está elevado a y, escreverei x^y, que é uma notação comum no meio científico.