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Walking up a steep hill, I pass 10 equally spaced street lamps. I take 5 seconds to walk from the first lamp to the second lamp, 6 seconds from the second lamp to the third, and so on, with each time increasing by 1 second as I slow down. How long do I take to walk from the first lamp to the last?

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*This problem is taken from the UKMT Mathematical Challenges.*

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