Among the numbers 1-100, how many times will the digit '7' occur? Among the numbers 1-1000 Class 6

Among the numbers 1-100, how many times will the digit '7' occur? Among the numbers 1-1000 Class 6

Question 1.

Among the numbers 1-100, how many times will the digit '7' occur? Among the numbers 1-1000, how many times will the digit '7' occur? Class 6

Solution:

(i) Among the numbers 1-100, digit '7' will occur in 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87 and 97. So, it will occurs 20 times.

(ii) Among the numbers 1-1000, digit '7' will occur in 7, 17, 27, ..., 79, 87, 97, 107, 117, 127, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 187, 197, 207, 217, 287, 297, 307, 317, 387, 397, 407, 417, ... 477, 478, 479, 487, 497, 507, 517, 587, 597, 607, 617, ... 687, 697, 700, 701, 702, 703, 704, 705, 706, 707, 717, 727, ..., 767, 777, 787, 797, 807, 817, ..., 887, 897, 907, 917, 987, 997.

In each of 1-100, 101-200, 201-300, 301- 400, 401-500, 501-600, 801-900 and 901- 1000, '7' will occur 20 times. Total 20 × 8 = 160 times.

In 601 to 700, '7' will occur 21 times.

In 701 to 800, '7' will occur (99+ 19 + 1) i.e., 119 times. So, in 1-1000, '7' will occur (160 + 21 +119) times i.e., 300 times.

Question 2.

Write all possible 3-digit palindromes using these digits. Class 6

Solution:

Other possible such 3-digit numbers are 111, 333, 131, 212, 232, 323.