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Think of a 2-letter word, for example, "AM." Write this word repeatedly in the given grid.

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{A} & \text{M} & \text{A} & \text{M} & \text{A} & \text{M} & \text{A} & \text{M} & \text{A} & \text{M} \\
1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\
\hline
21 & 22 & 23 & 24 & 25 & 26 & 27 & 28 & 29 & 30 \\
\hline
31 & 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 & 40 \\
\hline
\end{array}
\][/tex]

1. How many times do you write that word?

2. Write the numbers with the end letter of the word: 2, 4, 6, 8.

3. Repeat the above process for 3-letter and 4-letter words.

---

Note: The table provided in the original task is incomplete and contains inconsistencies. The grid above assumes a corrected and more straightforward pattern for illustration purposes.



Answer :

GinnyAnswer
Let's analyze and solve this problem step-by-step.

### 2-Letter Word: "AM"
1. Determine the grid size: We are working with a grid of size 40.
2. Word length: "AM" is 2 letters long.
3. Calculate the number of repetitions: The grid size (40) divided by the word length (2) equals 20. Thus, "AM" can be written 20 times in the grid.
4. End positions: Since "AM" is written 20 times, the end positions occur at each multiple of 2, i.e., 2, 4, 6, 8, ..., 40.

Hence, for the 2-letter word "AM," it is written 20 times, and the numbers with the end letter are:
[tex]\[ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 \][/tex]

### 3-Letter Word: "CAT"
1. Word length: "CAT" is 3 letters long.
2. Calculate the number of repetitions: The grid size (40) divided by the word length (3) yields another basis for calculation. While 40 ÷ 3 ≈ 13.33, we only consider whole numbers, so we take 13 as the number of full repetitions.
3. End positions: Since "CAT" is written 13 times, the end positions occur at each multiple of 3, rounding down for the final repetition: 3, 6, 9, 12, ..., 39.

Thus, for the 3-letter word "CAT," it is written 13 times, and the numbers with the end letter are:
[tex]\[ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 \][/tex]

### 4-Letter Word: "BIRD"
1. Word length: "BIRD" is 4 letters long.
2. Calculate the number of repetitions: The grid size (40) divided by the word length (4) equals 10. Thus, "BIRD" can be written 10 times in the grid.
3. End positions: Since "BIRD" is written 10 times, the end positions occur at each multiple of 4: 4, 8, 12, 16, ..., 40.

Therefore, for the 4-letter word "BIRD," it is written 10 times, and the numbers with the end letter are:
[tex]\[ 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 \][/tex]

Summarizing:
- For the 2-letter word "AM": Repetitions = 20, End positions = [tex]\( 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 \)[/tex]
- For the 3-letter word "CAT": Repetitions = 13, End positions = [tex]\( 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 \)[/tex]
- For the 4-letter word "BIRD": Repetitions = 10, End positions = [tex]\( 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 \)[/tex]

These calculations reflect how the words can be written throughout the grid and identify the positions at which each repetition ends.

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