Can you solve this question?

Question

There are 407 rooms in my hostel and I was assigned the work of numbering the rooms using plastic numbers. What is the number of plastic 3's needed to successfully number all rooms.

Answer 1

Think of 407 as being divided into 4 blocks of 100 (0-99. 100-199, 200-299, 300-399) - plus a few extra (400-407)

 

First think of threes in the ones digits (XX3) - for every block of 100, there are ten 3's in the ones digits (10 total), times 4 blocks of 100 = 10x4 = 40 (then add one more for room 403) = 41

 

Then think of threes in the tens digits (X3X) - for every block of 100, there are ten 3's in the tens digits (30-39), times 4 blocks of 100 = 10x4 = 40

 

Then think of threes in the hundreds digits (3XX) - there is only a 3 in the hundreds place for 300-399, which is 100 times

 

The total number of 3's then would be the ones + tens + hundreds = 41+40+100 = 181 threes