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7 votes

Define $R_n$ to be the maximum amount earned by cutting a rod of length $n$ meters into one or more pieces of integer length and selling them. For $i>0$, let $p[i]$ denote the selling price of a rod whose length is $i$ meters. Consider the array of prices:

$$\text{p}[1]=1,\text{p}[2]=5,\text{p}[3]=8,\text{p}[4]=9,\text{p}[5]=10,\text{p}[6]=17,\text{p}[7]=18$$Which of the following statements is/are correct about $R_7$?

- $R_7=18$
- $R_7=19$
- $R_7$ is achieved by three different solutions
- $R_7$ cannot be achieved by a solution consisting of three pieces

17 votes

A & C should be correct

- $1^{st}$ Solution $: p[2];p[3];p[2] = 5+8+5 = 18$
- $2^{nd}$ Solution $: p[7] = 18$
- $3^{rd}$ Solution $: p[6]; p[1] = 17+1 = 18$

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@debmalyaSEN Cutting a Rod into 1 piece = keeping the rod as a whole single piece. Hence it’s valid.

@unnayansharma p[2] just says the price of a piece of length 2. Imagine the rod is cut into 3 pieces of lengths : (2 units, 3 units, 2 units)

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