Grade 4 Slides, Flips and Turns

What this problem type covers

Ten problem types across five levels: reducing repeated flips and repeated turns, undoing a two-step slide, following grid commands and counting the coloured squares, combining two or three moves into one, reading a mirrored clock, tracking a marked square through a sequence of moves, and the digit-card problem where flipping and turning a number changes its value.

Example problems

One example from each difficulty band, with worked solutions.

Эти задачи создаются автоматически. Ответы определяются при составлении задачи и проверяются тестами, но ошибки возможны — сообщите нам, если найдёте.

1. 1 · ★1
   A shape is flipped right 4 times. Flipping the original right how many times gives the same result?
   • ①3 times
   • ②5 times
   • ③once
   • ④none (same as the original)
   • ⑤4 times
   Show solution

   ④none (same as the original)

   1. Flipping twice the same way returns the shape to the start.
   2. So pair the 4 flips up and see what is left over.
   3. 4 is even, so every flip pairs off.
   4. The result is the same as flipping none (same as the original).
2. 2 · ★2
   A point is moved down 6 cm, then right 7 cm. How must it be moved to get back to where it started?
   • ①left 7 cm, up 6 cm
   • ②up 6 cm, left 7 cm
   • ③down 6 cm, up 6 cm
   • ④left 7 cm, right 7 cm
   • ⑤down 6 cm, right 7 cm
   Show solution

   ①left 7 cm, up 6 cm

   1. To undo a move, reverse every direction.
   2. The order has to be reversed too, or it does not land back at the start.
   3. So undo the last move first: left 7 cm.
   4. Then up 6 cm, and it is back where it began.
3. 3 · ★3
   A shape is put through flipping up 4 times, then flipping down 4 times. Which single move applied to the original gives the same result?
   • ①the same as not moving it
   • ②a flip up or down
   • ③a 270° clockwise turn
   • ④a 180° clockwise turn
   • ⑤a 90° clockwise turn
   Show solution

   ①the same as not moving it

   1. Flipping twice the same way returns the shape, and a full turn changes nothing.
   2. So reduce the number of times each move is done first.
   3. That leaves the same as not moving it, then the same as not moving it.
   4. Doing those one after the other is the same as not moving it.
4. 4 · ★4
   A shape is put through turning 180° clockwise 2 times, then flipping right 4 times, then flipping up 3 times. Which single move applied to the original gives the same result?
   • ①a flip up or down
   • ②the same as not moving it
   • ③a 90° clockwise turn
   • ④a 270° clockwise turn
   • ⑤a 180° clockwise turn
   Show solution

   ①a flip up or down

   1. Flipping twice the same way returns the shape, and a full turn changes nothing.
   2. So reduce the number of times each move is done first.
   3. That leaves the same as not moving it, then the same as not moving it, then a flip up or down.
   4. Doing those one after the other is a flip up or down.
5. 5 · ★5
   On a 5 by 5 grid a star sits in row 2, column 4. After flipping left 1 times, then flipping down 1 times, then turning 90° clockwise 1 times, which square holds the star?
   
   • ①row 2, column 3
   • ②row 3, column 2
   • ③row 2, column 4
   • ④row 2, column 2
   • ⑤row 4, column 2
   Show solution

   ④row 2, column 2

   1. The grid is 5 wide, so a flip replaces a number with 6 minus it.
   2. A turn swaps the row number and the column number.
   3. Start at row 2, column 4 and follow the moves one at a time.
   4. The star ends up at row 2, column 2.

Where people usually go wrong

• Counting every flip. Two flips the same way return the shape, so only whether the count is odd or even matters.
• Forgetting a full turn changes nothing. 90° six times is 540°, which is the same as 180°.
• Undoing a slide without reversing the order. The last move has to be undone first.
• Counting a square twice when the path comes back to it.
• Flipping the digits without reversing their order, or reversing without flipping. A turn does one, a side flip does both.