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OlympiadBench / 2350 / Let f(n) be the number of positive integers that have exactly n digits and…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Let

f(n)

be the number of positive integers that have exactly

n

digits and whose digits have a sum of 5. Determine, with proof, how many of the 2014 integers

f(1), f(2), \ldots, f(2014)

have a units digit of 1 .

Plain-text mathematical notation (without MathML)

Let f(n) be the number of positive integers that have exactly n digits and whose digits have a sum of 5. Determine, with proof, how many of the 2014 integers f(1),f(2),…,f(2014) have a units digit of 1 .

Original LaTeX notation

Let $f(n)$ be the number of positive integers that have exactly $n$ digits and whose digits have a sum of 5. Determine, with proof, how many of the 2014 integers $f(1), f(2), \ldots, f(2014)$ have a units digit of 1 .

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2350
task_id: e337ca6c-0ffe-5241-afe9-ae984112e313
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2350
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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