benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Suppose that (a₁,b₁), (a₂,b₂), …, (a₁₀₀,b₁₀₀) are distinct ordered pairs of nonnegative integers. Let N denote the number of pairs of integers (i,j) satisfying 1≤i<j≤100 and …

Problem

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

problem

Suppose that (a1,b1),(a_1,b_1), (a2,b2),(a_2,b_2), …,\dots, (a100,b100)(a_{100},b_{100}) are distinct ordered pairs of nonnegative integers. Let NN denote the number of pairs of integers (i,j)(i,j) satisfying 1≤i<j≤1001\leq i<j\leq 100 and |aibj−ajbi|=1|a_ib_j-a_jb_i|=1. Determine the largest possible value of NN over all possible choices of the 100100 ordered pairs.
Plain-text mathematical notation (without MathML)
Suppose that (a₁,b₁), (a₂,b₂), …, (a₁₀₀,b₁₀₀) are distinct ordered pairs of nonnegative integers. Let N denote the number of pairs of integers (i,j) satisfying 1≤i<j≤100 and |a_(i)b_(j)−a_(j)b_(i)|=1. Determine the largest possible value of N over all possible choices of the 100 ordered pairs.
Original LaTeX notation
Suppose that $(a_1,b_1),$ $(a_2,b_2),$ $\dots,$ $(a_{100},b_{100})$ are distinct ordered pairs of nonnegative integers. Let $N$ denote the number of pairs of integers $(i,j)$ satisfying $1\leq i<j\leq 100$ and $|a_ib_j-a_jb_i|=1$. Determine the largest possible value of $N$ over all possible choices of the $100$ ordered pairs.

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
f7b9ee02-d4db-5459-906f-30f737cf1a84
task_key
test--f7b9ee02-d4db-5459-906f-30f737cf1a84
task_revision_id
1
config / split
/ test

Official source

initial import