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Omni-MATH / Let s(n) denote the sum of digits of a positive integer n. Using six different digits, we formed three 2-digits p,q,r such that p⋅q⋅s(r)=p⋅s(q)⋅r=s(p)⋅q⋅r. Find all such numbers …

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problem

Let s(n)s (n) denote the sum of digits of a positive integer nn. Using six different digits, we formed three 2-digits p,q,rp, q, r such that p⋅q⋅s(r)=p⋅s(q)⋅r=s(p)⋅q⋅r.p \cdot q \cdot s(r) = p\cdot s(q) \cdot r = s (p) \cdot q \cdot r. Find all such numbers p,q,rp, q, r.
Plain-text mathematical notation (without MathML)
Let s(n) denote the sum of digits of a positive integer n. Using six different digits, we formed three 2-digits p,q,r such that p⋅q⋅s(r)=p⋅s(q)⋅r=s(p)⋅q⋅r. Find all such numbers p,q,r.
Original LaTeX notation
Let $s (n)$ denote the sum of digits of a positive integer $n$. Using six different digits, we formed three 2-digits $p, q, r$ such that $$p \cdot q \cdot  s(r) = p\cdot s(q) \cdot r = s (p) \cdot q \cdot r.$$ Find all such numbers $p, q, r$.

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Source and history

task_id
eb2106ec-706a-56cd-a6e4-226118831888
task_key
test--eb2106ec-706a-56cd-a6e4-226118831888
task_revision_id
1
config / split
/ test

Official source

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