TACHS: Matrices: follow a dot that wraps
Learn to name a dot's square in its small grid, measure how it moves across and down the matrix, and wrap it around an edge without losing count.
How do you track a dot that slides off one edge of its grid and comes back on the other side?
Short answer
Name the dot's square by row and column, find the move across a row and the move down a column, and wrap any step that leaves the grid to the opposite edge. Predict the missing cell both ways.
Know first: Rows and columns in a grid, Left, right, up and down
Step 1 of 5
Name the square, then measure the move
In this kind of matrix, every cell holds the same small 3-by-3 grid with one dark dot in it. Moving one cell to the right moves the dot by a fixed step, such as one square right. Moving one cell down moves it by a different fixed step.
Give each square a two-word name: a row (top, middle, bottom) and a column (left, center, right). Middle right is easier to hold in your head than a picture.
| Move | From | Lands in |
|---|---|---|
| 1 right | right column | left column |
| 1 left | left column | right column |
| 1 up | top row | bottom row |
| 1 down | bottom row | top row |
| 2 right | any column | the same place as 1 left |
A move can also be diagonal, such as one right and one down. Handle the two parts separately.
Step 2 of 5
Track the dot across and down
| Column 1 | Column 2 | Column 3 | |
|---|---|---|---|
| Row 1 | top center | bottom center | middle center |
| Row 2 | top left | bottom left | middle left |
| Row 3 | top right | bottom right | ? |
Each entry names the square that holds the dot inside that cell's small grid.
Worked example: A dot that moves up and left
Use the matrix above. Where is the dot in the empty bottom-right cell?
- Amiddle center
- Bbottom right
- Cmiddle right
- Dmiddle left
- Etop right
- 1
Find the row move
Top row: top center, then bottom center, then middle center. From the top row, one step up wraps to the bottom row. One more step up gives the middle row. The row move is one square up.
- 2
Find the column move
First column: top center, then top left, then top right. One step left from the left column wraps to the right column. The column move is one square left.
- 3
Predict from the bottom row
The bottom row starts at top right, then bottom right. One more square up from bottom right gives middle right.
- 4
Check with the right column
The right column shows middle center, then middle left. One more square left from the left column wraps to the right: middle right. Both routes agree.
- 5
See why the other choices are there
Bottom right copies the cell to its left without moving the dot. Middle left stops at the edge in the right-column route instead of wrapping. Top right moves the dot down instead of up. Middle center applies the row move and the column move in the same step.
Answer
The dot is in the middle right square.
Wrong: Dot in the left column, move one square left: the dot stays at the left edge.
Right: Dot in the left column, move one square left: the dot wraps to the right column.
A dot never sticks at an edge in these matrices. It always wraps, and the wrap counts as one step.
Step 3 of 5
Move and wrap on your own
Check yourself · Question 1
The dot is in the middle right square of its small grid. Across the row, it moves one square right at each step. Where is it in the next cell?
Answer: B
One square right from the right column wraps to the left column. The row stays the same, so the dot lands in the middle left square.
| Column 1 | Column 2 | Column 3 | |
|---|---|---|---|
| Row 1 | bottom left | middle right | top center |
| Row 2 | bottom center | middle left | top right |
| Row 3 | bottom right | middle center | ? |
Each entry names the square that holds the dot inside that cell's small grid.
Check yourself · Question 2
Use the matrix above. Where is the dot in the empty bottom-right cell?
Answer: E
Across each row the dot moves one square up and one square left (bottom left to middle right wraps the column). Down each column it moves one square right. Bottom row: from middle center, one up and one left gives top left. Right column: from top right, one right wraps to the left column, top left. Both routes agree.
Trap answer: top right
Stopped at the edge
- Why it looks right
- The right column of the matrix shows top center, then top right. Staying put looks safer than jumping across the grid.
- Why it's wrong
- The column move is one square right. From the right column, that step wraps to the left column.
- The right answer
- top left, which the bottom-row route confirms.
Common mistake
I counted the wrap from the left column to the right column as two steps.
- Why it's tempting
- On paper the dot crosses the whole grid, so it feels like a long move.
- Do this instead
- A wrap is one step. In a grid three squares wide, one step left from the left column is the right column, and two steps right lands in the same place as one step left.
Step 4 of 5
What to remember
Remember
- Name each dot by row and column, such as middle right.
- Find the move across a row and the move down a column separately. A move can be diagonal.
- A step off an edge wraps to the opposite edge and counts as one step. Check the answer from both the bottom row and the right column.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
Try another one
In your own words
In the practice matrix, what is the move across a row and the move down a column, and where does a wrap happen?