Nine two-digit positive integers form an arithmetic progression. When the digits of each integer are reversed, the sum of the integers remains the same. The sum is
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Wait, so reversing the digits of every term doesn't change the total? That's such a neat property. How do I even start setting up the terms?
Same here, spent a minute just staring at it before I realized the condition is really restrictive.
Got it once I picked the middle term as the average. The AP makes the total 9 times the 5th term, so the reverse condition basically pins down the middle number. Nice one.
Ah right, odd number of terms means the middle term is the average. That simplifies everything.
Is this really 505-555? Felt more like a 600+ to me with the reversal twist. Took me way longer than I'd like to admit.
Agreed, the setup is the whole battle here.
Thanks, this was a good reminder that AP sum = number of terms × middle term when the count is odd. Saved me a ton of algebra.
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.