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MATH / Suppose we define ℓ(n) as follows: If n is an integer from 0 to 20, inclusive, then ℓ(n) is the number of letters in the English spelling of the number n; otherwise, ℓ(n) is undefi…

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problem

Suppose we define ℓ(n)\ell(n) as follows: If nn is an integer from 00 to 20,20, inclusive, then ℓ(n)\ell(n) is the number of letters in the English spelling of the number n;n; otherwise, ℓ(n)\ell(n) is undefined. For example, ℓ(11)=6,\ell(11)=6, because "eleven" has six letters, but ℓ(23)\ell(23) is undefined, because 2323 is not an integer from 00 to 20.20. How many numbers are in the domain of ℓ(n)\ell(n) but not the range of $\ell(n)?$
Plain-text mathematical notation (without MathML)
Suppose we define ℓ(n) as follows: If n is an integer from 0 to 20, inclusive, then ℓ(n) is the number of letters in the English spelling of the number n; otherwise, ℓ(n) is undefined. For example, ℓ(11)=6, because "eleven" has six letters, but ℓ(23) is undefined, because 23 is not an integer from 0 to 20.

How many numbers are in the domain of ℓ(n) but not the range of $\ell(n)?$
Original LaTeX notation
Suppose we define $\ell(n)$ as follows: If $n$ is an integer from $0$ to $20,$ inclusive, then $\ell(n)$ is the number of letters in the English spelling of the number $n;$ otherwise, $\ell(n)$ is undefined. For example, $\ell(11)=6,$ because "eleven" has six letters, but $\ell(23)$ is undefined, because $23$ is not an integer from $0$ to $20.$

How many numbers are in the domain of $\ell(n)$ but not the range of $\ell(n)?$

level

Level 5

type

Algebra

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Source and history

task_id
dd5fbbfa-3d08-5ee4-afd7-73a809a5cfd3
task_key
algebra--test--dd5fbbfa-3d08-5ee4-afd7-73a809a5cfd3
task_revision_id
1
config / split
algebra / test

Official source

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