benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let N be the number of functions f from {1,2,…,101}→{1,2,…,101} such that f¹⁰¹(1)=2. Find the remainder when N is divided by 103.

Problem

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

problem

Let NN be the number of functions ff from {1,2,…,101}→{1,2,…,101}\{1,2, \ldots, 101\} \rightarrow\{1,2, \ldots, 101\} such that f101(1)=2f^{101}(1)=2. Find the remainder when NN is divided by 103.
Plain-text mathematical notation (without MathML)
Let N be the number of functions f from {1,2,…,101}→{1,2,…,101} such that f¹⁰¹(1)=2. Find the remainder when N is divided by 103.
Original LaTeX notation
Let $N$ be the number of functions $f$ from $\{1,2, \ldots, 101\} \rightarrow\{1,2, \ldots, 101\}$ such that $f^{101}(1)=2$. Find the remainder when $N$ is divided by 103.

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
fb67ee34-e619-5b82-968f-66a0d84601de
task_key
test--fb67ee34-e619-5b82-968f-66a0d84601de
task_revision_id
1
config / split
/ test

Official source

initial import