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Omni-MATH / Three not necessarily distinct positive integers between 1 and 99, inclusive,…

Problem

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problem

Three not necessarily distinct positive integers between 1 and 99, inclusive, are written in a row on a blackboard. Then, the numbers, without including any leading zeros, are concatenated to form a new integer NN. For example, if the integers written, in order, are 25, 6, and 12, then N=25612N=25612 (and not N=250612N=250612). Determine the number of possible values of NN.
Plain-text mathematical notation (without MathML)
Three not necessarily distinct positive integers between 1 and 99, inclusive, are written in a row on a blackboard. Then, the numbers, without including any leading zeros, are concatenated to form a new integer N. For example, if the integers written, in order, are 25, 6, and 12, then N=25612 (and not N=250612). Determine the number of possible values of N.
Original LaTeX notation
Three not necessarily distinct positive integers between 1 and 99, inclusive, are written in a row on a blackboard. Then, the numbers, without including any leading zeros, are concatenated to form a new integer $N$. For example, if the integers written, in order, are 25, 6, and 12, then $N=25612$ (and not $N=250612$). Determine the number of possible values of $N$.

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Source and history

task_id
0ff830b8-1545-51fa-99fe-c0ae9d80f194
task_key
test--0ff830b8-1545-51fa-99fe-c0ae9d80f194
task_revision_id
1
config / split
/ test

Official source

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