benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / For any positive integer x, define Accident(x) to be the set of ordered pairs (s,t) with s∈{0,2,4,5,7,9,11} and t∈{1,3,6,8,10} such that x+s−t is divisible by 12. For any nonnegati…

Problem

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

problem

For any positive integer xx, define Accident(x)\operatorname{Accident}(x) to be the set of ordered pairs (s,t)(s, t) with s∈{0,2,4,5,7,9,11}s \in \{0,2,4,5,7,9,11\} and t∈{1,3,6,8,10}t \in\{1,3,6,8,10\} such that x+s−tx+s-t is divisible by 12. For any nonnegative integer ii, let aia_{i} denote the number of x∈{0,1,…,11}x \in\{0,1, \ldots, 11\} for which |Accident(x)|=i|\operatorname{Accident}(x)|=i. Find a02+a12+a22+a32+a42+a52a_{0}^{2}+a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}
Plain-text mathematical notation (without MathML)
For any positive integer x, define Accident(x) to be the set of ordered pairs (s,t) with s∈{0,2,4,5,7,9,11} and t∈{1,3,6,8,10} such that x+s−t is divisible by 12. For any nonnegative integer i, let a_(i) denote the number of x∈{0,1,…,11} for which |Accident(x)|=i. Find a₀²+a₁²+a₂²+a₃²+a₄²+a₅²
Original LaTeX notation
For any positive integer $x$, define $\operatorname{Accident}(x)$ to be the set of ordered pairs $(s, t)$ with $s \in \{0,2,4,5,7,9,11\}$ and $t \in\{1,3,6,8,10\}$ such that $x+s-t$ is divisible by 12. For any nonnegative integer $i$, let $a_{i}$ denote the number of $x \in\{0,1, \ldots, 11\}$ for which $|\operatorname{Accident}(x)|=i$. Find $$a_{0}^{2}+a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}$$

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
e6123736-c678-5d16-b358-678167c8ffe2
task_key
test--e6123736-c678-5d16-b358-678167c8ffe2
task_revision_id
1
config / split
/ test

Official source

initial import