benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Kelvin the Frog likes numbers whose digits strictly decrease, but numbers that…

Problem

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

problem

Kelvin the Frog likes numbers whose digits strictly decrease, but numbers that violate this condition in at most one place are good enough. In other words, if did_{i} denotes the ii th digit, then di≤di+1d_{i} \leq d_{i+1} for at most one value of ii. For example, Kelvin likes the numbers 43210, 132, and 3, but not the numbers 1337 and 123. How many 5-digit numbers does Kelvin like?
Plain-text mathematical notation (without MathML)
Kelvin the Frog likes numbers whose digits strictly decrease, but numbers that violate this condition in at most one place are good enough. In other words, if d_(i) denotes the i th digit, then d_(i)≤d_(i+1) for at most one value of i. For example, Kelvin likes the numbers 43210, 132, and 3, but not the numbers 1337 and 123. How many 5-digit numbers does Kelvin like?
Original LaTeX notation
Kelvin the Frog likes numbers whose digits strictly decrease, but numbers that violate this condition in at most one place are good enough. In other words, if $d_{i}$ denotes the $i$ th digit, then $d_{i} \leq d_{i+1}$ for at most one value of $i$. For example, Kelvin likes the numbers 43210, 132, and 3, but not the numbers 1337 and 123. How many 5-digit numbers does Kelvin like?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
cd6dc75f-52ac-5965-b935-8b8163c9292f
task_key
test--cd6dc75f-52ac-5965-b935-8b8163c9292f
task_revision_id
1
config / split
/ test

Official source

initial import