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Submit your answers to the following questions. Be sure to explain your reasoning for each. It is helpful to draw this out to see any quantitative patterns that develop.

1. If you write the counting numbers in rows of 7 numbers each, where all the numbers line up in seven vertical columns as you go, in which column would the number 100 land? In which row?

Example:
```
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
```

(Note: In the example above, the number 13 is in the 2nd row and the 6th column.)

2. Now write the counting numbers in rows of 6 numbers each. What’s the location of 100 in this array?

3. Write arrays with other length rows. Find a way to predict in which row and column the number 100 will land for any array of numbers.

Answer :

The number 100 would land in column 2

  • The number 100 would land in row 14
  • The location of 100 in rows of 6 numbers is row 16 and column 3
  • The location of 100 in rows of n numbers is row q and column r

In which column would the number 100 land?

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In which row would the number 100 land?

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

The location of 100 in rows of 6 numbers

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Predicting the row and column 100 will land

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

Read more about numbers at

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Rewritten by : Barada

The number 100 is in row 15 and column 2 when arranged in rows of 7. When arranged in rows of 6, it is in row 17 and column 4. These positions can be calculated for any row length using simple division and modulo operations.

Finding the Row and Column of the Number 100

To determine the row and column of the number 100 when counting numbers are arranged in rows of different lengths, follow these steps:

Rows of 7

If you write numbers in rows of 7, the row number is found by dividing the target number by the row length and rounding up, while the column number is determined by the remainder.

  1. Row number: 100 // 7 + 1 = 15
  2. Column number: 100 % 7 = 2

So, 100 is in row 15 and column 2.

Rows of 6

  1. Similarly, if you write numbers in rows of 6:
  2. Row number: 100 // 6 + 1 = 17

Column number: 100 % 6 = 4

Thus, 100 is in row 17 and column 4.

General Method for Any Row Length

For any array length n, follow these steps:

  1. Row number: (Target number // n) + 1
  2. Column number: (Target number % n) (if remainder is 0, the column is n)

For instance, for rows of 5:

  1. Row number: 100 // 5 + 1 = 21
  2. Column number: 100 % 5 = 0 (which means column 5)