The string of digits 135791113...999 is formed by merging together the decimal representations of the odd integers from 1 through 999. Counting from left, what is the 110th digit of this string of digits?
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This one took me way longer than it should have. I kept trying to "count" the odd numbers themselves instead of realizing you have to count digits. Once I bucketed by 1-digit, 2-digit, etc. it clicked, but the 110th position still felt tricky to pin down.
Same here. The off-by-one on where the position lands inside the number is what gets me every time.
Yeah the bucketing is the whole game. Took me a second attempt to trust my count.
Wait, I got to 55 odd numbers used up after the 2-digit block. Is the idea that we still need more digits after that, so we keep going into 3-digit numbers?
That's where I am too. Just have to be careful about how many digits are left and which odd number you land on.
Solid 655-705 level. Not hard conceptually but the digit indexing is a trap if you rush. Respect to anyone who nails this in under two minutes.
Small thing that helped me: write the cumulative digit counts as 5, then 90, then 450 before touching the actual numbers. Makes the 110th position obvious to place.
Good tip. I was doing it in my head and totally lost track.
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.