Study the pattern below carefully. If the pattern continues, what is the 99th99^{\text{th}} letter? SQUARESQUARESQUARE…1st18th\begin{matrix} \text{S} & \text{Q} & \text{U} & \text{A} & \text{R} & \text{E} & \text{S} & \text{Q} & \text{U} & \text{A} & \text{R} & \text{E} & \text{S} & \text{Q} & \text{U} & \text{A} & \text{R} & \text{E} & \dots \\ 1^{\text{st}} & & & & & & & & & & & & & & & & & 18^{\text{th}} \end{matrix} Ans : ___

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Worked solution

22

1. Identify the repeating pattern and its length

The pattern is 'S Q U A R E', which repeats every 6 letters.

2. Find the position of the 99th letter within the cycle

99÷6=1699 \div 6 = 16 with a remainder of 33.

3. Determine the letter corresponding to the remainder

A remainder of 3 means the 99th99^{\text{th}} letter is the 3rd3^{\text{rd}} letter in the pattern 'S Q U A R E', which is 'U'.

Answer

U

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