Position and Motion Quiz

A. 2

The marker finishes at 2. After the final numbered position, counting continues at zero rather than outside the track. Following each step or reducing the total advance by a full track length gives the same result.

Try next: Trace the exact position after every forward step.

B. Valid

Every intermediate position remains inside the permitted range. The route is therefore valid. A later return cannot repair an earlier boundary violation because validity applies at every step.

Try next: Write the running positions and underline the first violation, if any.

C. 0

The final row is 0. A MOVE attempts one step in the current gravity direction, but an edge prevents going farther. FLIP changes later movement direction while leaving the current row unchanged.

Try next: Track row and gravity in separate columns after every command.

A. 3

Reflection places the marker in column 3, the same distance from the opposite edge. Reflected column pairs sum to 4. This differs from shifting the marker a fixed number of steps along the row.

Try next: List the reflected pairs from both edges toward the center.

B. 2

The positions become 2 and 4, so the separation is 2. Each round reduces their initial separation by two until they meet. Both markers move, so counting only one marker’s distance gives the wrong gap.

Try next: Draw both trajectories on the same numbered line.

C. east

The arrow ends pointing east. Opposite quarter-turns cancel, leaving a net rotation of 1 clockwise quarter-turns. Negative net rotation means counterclockwise movement; a full group of four turns has no lasting effect.

Try next: Perform the rotations in reverse group order and compare the final direction.

A. (1, 0)

The final coordinate is (1, 0). Right and left moves affect only x; up and down affect only y. Opposite moves cancel within the same coordinate, while horizontal movement cannot cancel a vertical move.

Try next: Separate the command list into horizontal and vertical subtotals.

B. 0

The phases have 6 visits across 6 available checkpoints, with 0 shared checkpoints. Here the two ranges meet without overlapping. A visit count and a distinct checkpoint count are different quantities.

Try next: Number the checkpoints and mark each phase in a different symbol.

C. 7

7 advances reach position 14, meeting the finish condition. One fewer reaches only 12, which is short. Rounding upward is necessary because a partial command cannot be issued under these movement rules.

Try next: Compare this answer with a version requiring an exact landing.

A. 4

The marker finishes at 4. After the final numbered position, counting continues at zero rather than outside the track. Following each step or reducing the total advance by a full track length gives the same result.

Try next: Trace the exact position after every forward step.

B. Invalid

At least one intermediate step leaves the permitted range. The route is therefore invalid. A later return cannot repair an earlier boundary violation because validity applies at every step.

Try next: Write the running positions and underline the first violation, if any.

C. 0

The final row is 0. A MOVE attempts one step in the current gravity direction, but an edge prevents going farther. FLIP changes later movement direction while leaving the current row unchanged.

Try next: Track row and gravity in separate columns after every command.

A. 4

Reflection places the marker in column 4, the same distance from the opposite edge. Reflected column pairs sum to 6. This differs from shifting the marker a fixed number of steps along the row.

Try next: List the reflected pairs from both edges toward the center.

B. 0

The positions become 4 and 4, so the separation is 0. Each round reduces their initial separation by two until they meet. Both markers move, so counting only one marker’s distance gives the wrong gap.

Try next: Draw both trajectories on the same numbered line.

C. east

The arrow ends pointing east. Opposite quarter-turns cancel, leaving a net rotation of 2 clockwise quarter-turns. Negative net rotation means counterclockwise movement; a full group of four turns has no lasting effect.

Try next: Perform the rotations in reverse group order and compare the final direction.

A. (0, 1)

The final coordinate is (0, 1). Right and left moves affect only x; up and down affect only y. Opposite moves cancel within the same coordinate, while horizontal movement cannot cancel a vertical move.

Try next: Separate the command list into horizontal and vertical subtotals.

B. 2

The phases have 10 visits across 8 available checkpoints, with 2 shared checkpoints. Here the two ranges overlap by the stated excess. A visit count and a distinct checkpoint count are different quantities.

Try next: Number the checkpoints and mark each phase in a different symbol.

C. 7

7 advances reach position 21, meeting the finish condition. One fewer reaches only 18, which is short. Rounding upward is necessary because a partial command cannot be issued under these movement rules.

Try next: Compare this answer with a version requiring an exact landing.

A. 5

The marker finishes at 5. After the final numbered position, counting continues at zero rather than outside the track. Following each step or reducing the total advance by a full track length gives the same result.

Try next: Trace the exact position after every forward step.

B. Invalid

At least one intermediate step leaves the permitted range. The route is therefore invalid. A later return cannot repair an earlier boundary violation because validity applies at every step.

Try next: Write the running positions and underline the first violation, if any.

C. 0

The final row is 0. A MOVE attempts one step in the current gravity direction, but an edge prevents going farther. FLIP changes later movement direction while leaving the current row unchanged.

Try next: Track row and gravity in separate columns after every command.

A. 5

Reflection places the marker in column 5, the same distance from the opposite edge. Reflected column pairs sum to 8. This differs from shifting the marker a fixed number of steps along the row.

Try next: List the reflected pairs from both edges toward the center.

B. 0

The positions become 6 and 6, so the separation is 0. Each round reduces their initial separation by two until they meet. Both markers move, so counting only one marker’s distance gives the wrong gap.

Try next: Draw both trajectories on the same numbered line.

C. west

The arrow ends pointing west. Opposite quarter-turns cancel, leaving a net rotation of -2 clockwise quarter-turns. Negative net rotation means counterclockwise movement; a full group of four turns has no lasting effect.

Try next: Perform the rotations in reverse group order and compare the final direction.

A. (0, -1)

The final coordinate is (0, -1). Right and left moves affect only x; up and down affect only y. Opposite moves cancel within the same coordinate, while horizontal movement cannot cancel a vertical move.

Try next: Separate the command list into horizontal and vertical subtotals.

B. 3

The phases have 13 visits across 10 available checkpoints, with 3 shared checkpoints. Here the two ranges overlap by the stated excess. A visit count and a distinct checkpoint count are different quantities.

Try next: Number the checkpoints and mark each phase in a different symbol.

C. 7

7 advances reach position 28, meeting the finish condition. One fewer reaches only 24, which is short. Rounding upward is necessary because a partial command cannot be issued under these movement rules.

Try next: Compare this answer with a version requiring an exact landing.