PEA 2024 PEA Q14 | ISI MSQE

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2024 PEA Q14

A monkey starts at $(0,0)$ on the $xy$ -plane in period $1$ . From any position $(x,y)$ in a period, the monkey can only jump to $(a,b)$ in the next period, where $a\in\{x+1,x,x-1\}$ and $b\in\{y+1,y,y-1\}$ . How many possible positions can the monkey be in period $2$ ?

Reveal answer and solution

Answer

Solution

1
$a$ has $3$ possible values and $b$ has $3$ possible values, and they are independent. So the number of reachable positions $=3\times 3=9$ .

Answer structure / marking notes

No major trap beyond standard calculation care.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2024/ISI_MSQE_PEA_2024_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.