1. Make or write the number 42,019. It would require exactly 23 sticks. 2. Starting with 42,019, add or write two more sticks, and make a bigger number. One example is 42,078. What other numbers bigger than 42,019 can you make in this way? 3. Preetham wants to insert the digit '1' somewhere among the digits '4', '2', '0', '1' and '9'. Where should he place the digit '1' to get the biggest possible number? 4. What other numbers can he make by placing the digit '1'?

Understand the Question Matchstick digits are constructed using standard digital display (7-segment) representations. The number of matchsticks required for each digit is: Digit : Digit : Digit : Digit : Digit : Digit : Digit : Digit : Digit : Digit : Using these segment counts, we can determine total stick requirements, form new numbers by adding sticks, and find the largest permutations by inserting a new digit. Part 1. Make or write the number 42,019. It would require exactly 23 sticks. Step 1 · Count Sticks for 42,019 Segments used by each digit in : Digit '4': Digit '2': Digit '0': Digit '1': Digit '9': Total sticks needed: Answer > 1. Part 2. Starting with 42,019, add or write two more sticks, and make a bigger number. One example is 42,078. What other numbers bigger than 42,019 can you make in this way? Step 1 · Form Numbers with 25 Sticks Adding sticks requires using a total of . Case 1: Adding 2 sticks to a single digit Change '4' () '6' (): Change '4' () '9' (): Change '2' () '8' (): Change '1' () '4' (): Case 2: Adding 1 stick each to two different digits Changing single digits by : '4' '5', '0' '8', '1' '7', '9' '8'. Combining two changes: '4' '5' and '1' '7': '0' '8' and '1' '7': '4' '5' and '9' '8': Answer > 2. Part 3. Preetham wants to insert the digit '1' somewhere among the digits '4', '2', '0', '1' and '9'. Where should he place the digit '1' to get the biggest possible number? Step 1 · Compare Placements of Digit '1' Inserting digit '1' into at different positions yields: Before '4': Between '4' and '2': Between '2' and '0': Between '0' and '1': Between '1' and '9': After '9': Comparing these values from the highest place value, the largest number is . Answer > 3. Between '2' and '0' to get Part 4. What other numbers can he make by placing the digit '1'? Step 1 · List Other Formed Numbers From the possible insertions, the remaining unique numbers formed are: Answer > 4. Common Mistakes Duplicate Counts: Inserting '1' between '0' and '1' vs. between '1' and '9' yields the exact same number (); avoid listing it twice as distinct numbers. Incorrect Stick Additions: Confusing which digits can form valid matchstick numbers with or sticks (e.g., changing '0' with sticks directly into '8' with sticks is , not ). Place Value Misunderstanding: Placing '1' at the very beginning creates a smaller -digit number () than keeping '4' and '2' in the highest place value positions ().

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Question 5

Make or write the number 42,019. It would require exactly 23 sticks.
Starting with 42,019, add or write two more sticks, and make a bigger number. One example is 42,078. What other numbers bigger than 42,019 can you make in this way?
Preetham wants to insert the digit '1' somewhere among the digits '4', '2', '0', '1' and '9'. Where should he place the digit '1' to get the biggest possible number?
What other numbers can he make by placing the digit '1'?

Solution

Understand the Question

Matchstick digits are constructed using standard digital display (7-segment) representations. The number of matchsticks required for each digit is:

Digit $0$ : $6\text{ sticks}$
Digit $1$ : $2\text{ sticks}$
Digit $2$ : $5\text{ sticks}$
Digit $3$ : $5\text{ sticks}$
Digit $4$ : $4\text{ sticks}$
Digit $5$ : $5\text{ sticks}$
Digit $6$ : $6\text{ sticks}$
Digit $7$ : $3\text{ sticks}$
Digit $8$ : $7\text{ sticks}$
Digit $9$ : $6\text{ sticks}$

Using these segment counts, we can determine total stick requirements, form new numbers by adding sticks, and find the largest permutations by inserting a new digit.

1. Make or write the number 42,019. It would require exactly 23 sticks.

Step 1 · Count Sticks for 42,019

Diagram 1

Segments used by each digit in $42{,}019$ :

Digit '4': $4\text{ sticks}$
Digit '2': $5\text{ sticks}$
Digit '0': $6\text{ sticks}$
Digit '1': $2\text{ sticks}$
Digit '9': $6\text{ sticks}$

Total sticks needed: $4 + 5 + 6 + 2 + 6 = 23$

Answer

1. $23\text{ sticks}$

2. Starting with 42,019, add or write two more sticks, and make a bigger number. One example is 42,078. What other numbers bigger than 42,019 can you make in this way?

Step 1 · Form Numbers with 25 Sticks

Diagram 2

Adding $2$ sticks requires using a total of $23 + 2 = 25\text{ sticks}$ .

Case 1: Adding 2 sticks to a single digit

Change '4' ( $4$ ) $\to$ '6' ( $6$ ): $62{,}019$
Change '4' ( $4$ ) $\to$ '9' ( $6$ ): $92{,}019$
Change '2' ( $5$ ) $\to$ '8' ( $7$ ): $48{,}019$
Change '1' ( $2$ ) $\to$ '4' ( $4$ ): $42{,}049$

Case 2: Adding 1 stick each to two different digits

Changing single digits by $+1\text{ stick}$ : '4' $\to$ '5', '0' $\to$ '8', '1' $\to$ '7', '9' $\to$ '8'.
Combining two changes:
- '4' $\to$ '5' and '1' $\to$ '7': $52{,}079$
- '0' $\to$ '8' and '1' $\to$ '7': $42{,}879$
- '4' $\to$ '5' and '9' $\to$ '8': $52{,}018$

Answer

2. $62{,}019,\; 92{,}019,\; 48{,}019,\; 42{,}049,\; 52{,}079,\; 42{,}879,\; 52{,}018$

3. Preetham wants to insert the digit '1' somewhere among the digits '4', '2', '0', '1' and '9'. Where should he place the digit '1' to get the biggest possible number?

Step 1 · Compare Placements of Digit '1'

Diagram 3

Inserting digit '1' into $42{,}019$ at different positions yields:

Before '4': $142{,}019$
Between '4' and '2': $412{,}019$
Between '2' and '0': $421{,}019$
Between '0' and '1': $420{,}119$
Between '1' and '9': $420{,}119$
After '9': $420{,}191$

Comparing these values from the highest place value, the largest number is $421{,}019$ .

Answer

3. Between '2' and '0' to get $421{,}019$

4. What other numbers can he make by placing the digit '1'?

Step 1 · List Other Formed Numbers

From the possible insertions, the remaining unique numbers formed are:

$142{,}019$
$412{,}019$
$420{,}119$
$420{,}191$

Answer

4. $142{,}019,\; 412{,}019,\; 420{,}119,\; 420{,}191$

Common Mistakes

Duplicate Counts: Inserting '1' between '0' and '1' vs. between '1' and '9' yields the exact same number ( $420{,}119$ ); avoid listing it twice as distinct numbers.
Incorrect Stick Additions: Confusing which digits can form valid matchstick numbers with $+1$ or $+2$ sticks (e.g., changing '0' with $6$ sticks directly into '8' with $7$ sticks is $+1\text{ stick}$ , not $+2$ ).
Place Value Misunderstanding: Placing '1' at the very beginning creates a smaller $6$ -digit number ( $142{,}019$ ) than keeping '4' and '2' in the highest place value positions ( $421{,}019$ ).

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