Sum of k-Mirror Numbers
A hard-tier problem at 42% community acceptance, tagged with Math, Enumeration. Reported in interviews at Cisco and 0 others.
Sum of k-Mirror Numbers is a hard problem that shows up in Cisco interviews. It asks you to find all k-mirror numbers below a given limit and return their sum. A k-mirror number is a number whose representation in base 10 and base k are both palindromes. The 41% acceptance rate reflects the fact that most candidates misjudge the enumeration strategy. You need to generate palindromes efficiently rather than check every integer. If you hit this during a live assessment and the enumeration pattern doesn't click, StealthCoder surfaces a working solution instantly.
Companies that ask "Sum of k-Mirror Numbers"
Sum of k-Mirror Numbers is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Built by an engineer who got tired of watching his cohort grind for six months and still get filtered at the OA stage.
Get StealthCoderThe trap is brute force: iterate through numbers, convert to base k, check if both representations are palindromes. That's slow and wrong on large limits. The real trick is to enumerate palindromes in base 10 directly, then validate each one in base k. You construct palindromes by taking the first half of a number and mirroring it. For each candidate palindrome, convert it to base k and check if that's also a palindrome. Common pitfall: off-by-one errors in base conversion or palindrome construction. Another: forgetting to handle single-digit numbers (they're always palindromes in any base). The enumeration approach drops time complexity dramatically. When you're live and the enumeration isn't obvious, StealthCoder handles the base conversion and palindrome check logic instantly.
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Sum of k-Mirror Numbers recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Built by an engineer who got tired of watching his cohort grind for six months and still get filtered at the OA stage. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Sum of k-Mirror Numbers interview FAQ
Why can't I just iterate and check every number?+
You can, but it times out on large limits. A number and its base-k representation both need to be palindromes. Most integers fail that test, so you're wasting cycles. Enumerating palindromes in base 10 first, then validating in base k, is exponentially faster.
How do I generate palindromes efficiently?+
Build them from their first half. For a 5-digit palindrome, take a 3-digit number, mirror the first two digits onto the end. For even-length palindromes, mirror all digits. Iterate through half-lengths and seed values, construct full palindromes, validate in base k.
Is base conversion the hard part?+
It's error-prone but straightforward. Repeatedly divide by k, collect remainders, reverse the result. Store remainders as a list of digits, not a string, so you can check palindrome without string operations. Test your conversion logic early.
What about single-digit numbers?+
They're palindromes in any base. Don't skip them. All numbers 1-9 are valid k-mirror numbers for any k >= 2. Make sure your enumeration includes the single-digit case.
Cisco asks this, but how often does it appear in reports?+
It's a lower-frequency problem overall. The 41% acceptance rate suggests it's less drilled than standard medium-level problems. If you see it on your assessment, it's likely a Cisco-specific ask. That's when the enumeration trick becomes critical.
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