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Omni-MATH / Find all permutations a₁,a₂,…,a₉ of 1,2,…,9 such that a₁+a₂+a₃+a₄=a₄+a₅+a₆+a₇=a₇+a₈+a₉+a₁ and a₁²+a₂²+a₃²+a₄²=a₄²+a₅²+a₆²+a₇²=a₇²+a₈²+a₉²+a₁²

Problem

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

problem

Find all permutations a1,a2,…,a9a_1, a_2, \ldots, a_9 of 1,2,…,91, 2, \ldots, 9 such that a1+a2+a3+a4=a4+a5+a6+a7=a7+a8+a9+a1 a_1+a_2+a_3+a_4=a_4+a_5+a_6+a_7= a_7+a_8+a_9+a_1 and a12+a22+a32+a42=a42+a52+a62+a72=a72+a82+a92+a12 a_1^2+a_2^2+a_3^2+a_4^2=a_4^2+a_5^2+a_6^2+a_7^2= a_7^2+a_8^2+a_9^2+a_1^2
Plain-text mathematical notation (without MathML)
Find all permutations a₁,a₂,…,a₉ of 1,2,…,9 such that  a₁+a₂+a₃+a₄=a₄+a₅+a₆+a₇=a₇+a₈+a₉+a₁
and
a₁²+a₂²+a₃²+a₄²=a₄²+a₅²+a₆²+a₇²=a₇²+a₈²+a₉²+a₁²
Original LaTeX notation
Find all permutations $a_1, a_2, \ldots, a_9$ of $1, 2, \ldots, 9$ such that  \[ a_1+a_2+a_3+a_4=a_4+a_5+a_6+a_7= a_7+a_8+a_9+a_1 \]
and
\[ a_1^2+a_2^2+a_3^2+a_4^2=a_4^2+a_5^2+a_6^2+a_7^2= a_7^2+a_8^2+a_9^2+a_1^2 \]

Discussion

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Source and history

task_id
5cba2fb5-69fc-54cd-8e0c-eab07dc276a2
task_key
test--5cba2fb5-69fc-54cd-8e0c-eab07dc276a2
task_revision_id
1
config / split
/ test

Official source

initial import