Question

1) a) Cite numere naturale de forma 3aa exista? b) Cite numere naturale de forma 5ab, cu a si b distincte, exista? c) Cite numere naturale de forma 5ab exista? d) Cite numere naturale de forma a5b exista? Dau coroana.

Answer 1

a) 3aa, a poate avea valori {0,1, 2......, 9} deci 10 numere
300; 311; 322; 333; 344; 355; 366; 377; 388; 399

b)
a poate avea valori {0,1, 2......, 9} deci 10 numere
si
b poate avea valori {0,1, 2......, 9} deci 10 numere

10 x 10 = 100 numere dar dispar cere care se dubleaza, deoarece acest punct cere distincte, deci din 100 scadem 10= 90
c)
a poate avea valori {0,1, 2......, 9} deci 10 numere
si
b poate avea valori {0,1, 2......, 9} deci 10 numere

10 x 10 = 100 numere

d) a5b
a poate avea valori {1, 2......, 9} deci 9 numere 9 poate lua valoarea 0
si
b poate avea valori {0,1, 2......, 9} deci 10 numere

9 x 10 = 90 numere

Answer 2

a) 3aa: 300, 311, 322,333, 344, 355, 366, 377, 388, 399;
b) 5ab: 501,510,502, 520,503, 530, 504, 540, 505,550, 506,560, 507,570,508,580,509,590
c) 5ab:501, 502,503,504,505,506,507,508,509,510,512,513,514,516,517,518, 519,520,521,523,524,525,526, 527,528,529,530,531,532, 534,535,536,537,538,539,540,541,542,543,544, 546,547,548,549,550,551,552,553,554,556,557,558,559,560,561,562,563,564,565,567,568,569,570,571,571,572,573,574,576,578,579,580,582,583,584,586,587,589,590,591,592,593,594,595,596,597,598;
d)a5b: 150,152,153,154,156,157,158,159, 250,251,253,254,256,257,258,,259,350,351,352, 354,356,357,358,359,450,451, 452,453,456,457,458,459,650,651,652,m653,654,657,658,659, 750,751,752,753,754,758,759,850,851,852,853,854,856,857,859.950,951,952,953,954,956,957,958.