Question

Find the sum of all 3's that are needed to write the number from 200 to 400.

Answer 1

Answer:

420

Step-by-step explanation:

Consider the numbers from 200 to 299. The numbers having 3 in the units place are 203, 213, 223, ... , 293  10 numbers. The numbers having 3 in the tens place are 230, 231, 232, ..., 239  10 numbers. The numbers having 3 in the hundreds place are 0. Consider the numbers from 300 to 400, the numbers having 3 in the units place are 10. Again, the numbers having 3 in the tens place are 10 and the numbers having 3 in the hundreds place are 300, 301, 302, ..., 399  100 numbers. Hence, there are totally 10 + 10 + 10 + 10 +100 = 140 3's in all the specified numbers.  The required sum = 140 x 3 = 420. Hence, 420

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