ITPEC IP October 2020 Question 6

Topic: Algorithm and ProgrammingAlso asked in October 2018, October 2022, April 2024 and April 2026

There exist four (4) states numbered 1 through 4. The four (4) states are connected as shown in the figure below, and the state transition occurs in a clockwise or counter-clockwise direction.

1234

If the current state is 1, which of the following states is reached after the procedure below is performed twice?

[Procedure]

The number of the current state is multiplied by 11, and the result is divided by 3. The process below is performed based on the remainder of the division.

•When the remainder is 0, a transition to the next state occurs in the clockwise direction.•When the remainder is 1, a transition to the next state occurs in the counter-clockwise direction.•When the remainder is 2, a transition to the state after the next state occurs in the clockwise direction.

Explanation

4 — the first procedure moves 1 → 3 and the second 3 → 4, with the remainder recomputed from the new state each time.

Clockwise, the states run 1 → 2 → 3 → 4 → 1.

  • •First run, state 1: 1 × 11 = 11, and 11 ÷ 3 = 3 remainder 2, so move to the second state clockwise: 1 → 2 → 3
  • •Second run, state 3: 3 × 11 = 33, and 33 ÷ 3 = 11 remainder 0, so move to the next state clockwise: 3 → 4

Answer (d)

Why not others:

  • •(a) 1 — reuses the first remainder, 2, in the second run: two more states clockwise from 3 lands back on 1
  • •(b) 2 — takes remainder 0 as counter-clockwise, moving 3 → 2
  • •(c) 3 — the state after the first run only; the procedure is performed twice

Key rule: When a rule depends on the current state, recompute it after every transition instead of carrying the first result forward.

Algorithm and Programming · AI-written, may contain errors

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