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Home » Let the two quantities be \( a \) and \( b \). We are given: - Londonproperty

Let the two quantities be \( a \) and \( b \). We are given: - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Is there a smaller two-digit value? Next smaller would be $ m = -1 $: $ L = 91(-1) + 14 = -77 $, not positive.

📌 So 14 is the smallest.

📌 But wait: is 14 a valid total length made from 7-unit pipes? Yes: two pipes â $ 7 imes 2 = 14 $.

📌 Thus, the smallest two-digit total length satisfying the condition is $ oxed{14} $.

📌 Question: A primatologist observes that a troop of monkeys communicates using sequences of calls, each lasting a prime number of seconds. If the total duration of a sequence longer than 20 seconds but less than 40 seconds consists of the sum of distinct prime-numbered call durations, what is the largest possible total duration?

📌 Solution: We seek the largest integer $ N $ such that $ 20 < N < 40 $, and $ N $ is the sum of distinct prime numbers.

📌 We aim for the largest such $ N $, so start from 39 downward.

📌 Check if 39 can be written as sum of distinct primes:

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