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UKMT Junior Kangaroo, 2021

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Andrew wants to write the letters of the word KANGAROO in the cells of a 2×42 \times 4 grid such that each cell contains exactly one letter. He can write the first letter in any cell he chooses but each subsequent letter can only be written in a cell with at least one common vertex with the cell in which the previous letter was written. Which of the following arrangements of letters could he not produce in this way?

(A) Grid (rows top to bottom): K A / N O / O G / R A (B) Grid (rows top to bottom): N G / A A / K R / O O (C) Grid (rows top to bottom): O O / K R / A A / G N (D) Grid (rows top to bottom): K A / N G / O O / R A (E) Grid (rows top to bottom): K O / A O / R N / A G

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