A number theory problem by Pramit Nandy
The micromanometer of a factory can measure pressure from 1 to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micronanometer displays 003016 ?
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1 solution
Since, it skipped all the numbers that had 5 in it. We need to remove all the numbers from 1 to 3016 which had 5 in it and subtract it from 3016.
- 1-digit number : _ only 1 is possible i.e. 5
- 2-digit number : _ _ If 5 is at units place, then 8x1(because 0 at tens place will give a single digit) and if at tens place, then 9x1 and if both are 5 then 1x1 = 1x9+8x1 + 1x1 = 18
- 3-digit number : _ _ _ = 1x9x9 + 8x1x9 + 8x9x1 + 1x1x9 + 8x1x1 + 1x9x1 + 1x1x1 = 252
- 4-digit number : _ _ _ _ = To find this, break numbers into 1000 - 2999 and then 3000- 3016. Then, 2x9x9x1 + 2x9x1x9 + 2x1x9x9 + 2x1x1x9 + 2x9x1x1 +2x1x9x1+ 2x1x1x1 and 1x1x2x1 = 524 and 2.
So, total numbers with 5 in it = 1+18+252+542+2 = 815