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Home » Round up to 20 cones. - Silent Sales Machine

Round up to 20 cones. - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Since positions are from 1 to 5, the possible values are limited.

📌 We can iterate over possible \( r_{\max} = m \) and \( l_{\min} = k \) with \( m < k \).

📌 Possible values: \( m \) ranges from 2 to 4, and for each \( m \), \( k \) ranges from \( m+1 \) to 5.

📌 But \( k \geq m+1 \), and \( m \geq 2 \), \( k \leq 5 \).

📌 For each such pair (m, k), we count the number of ways:

📌 Choose 2 distinct positions for R’s: both < m? No: R’s must be all \( < k \), and max \( R \leq m \), and \( m < k \), so all R positions ∈ [1, m-1]? No: if \( k \geq m+1 \), we need R’s all < k, but \( m < k \), so R’s can be in [1, k−1], but they must all be < k and their max < k, but we require max R < k — always true if R’s are in [1, k−1]. But we need **both R’s < k**, which is automatic if we choose from 1 to k−1, but the condition is only upper bound on L’s.

📌 Wait — correction: we need **all R’s before all L’s**, i.e., every R position < every L position.

📌 So: max(R) < min(L)

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