Problem 4 · 2009 Math Kangaroo
Easy
Number Theory
careful-counting
What is the smallest number of digits that must be removed from the number 12323314 so that the number left over reads the same forwards and backwards?
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Answer: C — 3
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Hint 1 of 2
A palindrome reads the same forwards and backwards; keep the longest such block you can.
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Hint 2 of 2
Removing digits is fastest when you keep the longest in-order palindrome and delete the rest.
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Approach: keep longest palindrome, delete the rest
- The number is 1 2 3 2 3 3 1 4.
- The longest run of digits that stays in order and reads the same both ways has length 5 (for example 1 2 3 2 1).
- Eight digits minus that 5 leaves 3 to remove.
- Minimum removed = 3 — answer C.
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