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📰 Solution: We are looking for the smallest two-digit positive integer $ L $ such that 📰 L \equiv 1 \pmod{13} 📰 and $ L $ is a multiple of 7 (since pipes are seven units long and total length is a sum of such pipes). However, note: the problem states the *total length of installed pipe* is one more than a multiple of 13—so $ L \equiv 1 \pmod{13} $, and $ L $ must be expressible as a sum of multiples of 7. But since individual pipes are 7 units, any valid total length must be a multiple of 7. So we seek the smallest two-digit number $ L $ such that: 📰 Free Fun Thatll Make You Laugh Youll Want To Share This Instant Joy 1574015 📰 Film Pitch Perfect 2 1191132 📰 Unity Symbol Revealed 7 Powerful Meanings You Need To Know Before It Goes Viral 2639110 📰 Natures Palette Discover The Most Stunning Natural Hair Color Trends Of 2024 9836948 📰 Lich Wont Stop Timeheres The Untold Secrets Of Adventure Times Deadly Foe 2265085 📰 Barrio Logan 1460453 📰 Why Idfc First Banks Stock Is Skyrocketinginvest Now Before It Hits New Heights 9427022 📰 Istatistica 5783419 📰 City Of Bedford Water 4671378 📰 Alice Beck Dubow Exposed Her Shocking Secret No One Should Believe 6832262 📰 Todays 30 Year Mortgage Rate 1612875 📰 Best Auto Insurance Colorado 3417821 📰 The Making Of Anglo Saxon England From Tribal Society To Early Kingdom Oxford University Press 2020 986112 📰 432 Park 3351455 📰 Step By Step Unique College Investing Plan Guaranteed To Boost Your Next Generations Wealth 3653301