3 or 9

Number Theory Level 2

How many numbers are there between 100 and 1000, such that the digits are either 3 or 9?


The answer is 8.

Shamima Shimu by Shamima Shimu , 39, Bangladesh

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3 solutions

Muhammed Naseef
May 22, 2014

The numbers are 333, 339, 393, 399, 933, 939, 993, 999.

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Shamima Shimu
May 17, 2014

All numbers between 100 and 1000 are of three digits & digits which are to be used are 3 or 9.

Unit's place can be filled in 2 ways either by 3 or 9. Similarly, tenth place can be filled in 2 ways

& Hundredth place can be filled in two ways,

Therefore, total numbers which are between 100 and 1000 such that every digit is either 3 or 9

= 2 * 2 * 2 = 8

The numbers are 333, 339, 393, 399, 933, 939, 993, 999

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Since there are two choices for each of the 3 3 digits, there are 2 ⋅ 2 ⋅ 2 = 8 2 \cdot 2 \cdot 2 = 8 such numbers.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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