QuestionWhat is the largest 5-digit number Noe Noe could think of if Toe Toe's guesses 20489 and 15673 reveal 2 and 3 correct digits, respectively?

Studdy Solution

STEP 1

Assumptions1. Noe Noe's number is a5-digit number. . Toe Toe's first guess is20489 and exactly two digits are correct and in their right place.
3. Toe Toe's second guess is15673 and exactly three digits are correct and in their right place.

STEP 2

We need to find the common digits in the correct place in both guesses. These digits are0 in the second place and8 in the fourth place.
$20489$ $15673$

STEP 3

Now, we know that the second and fourth digits of Noe Noe's number are0 and8 respectively. The number now looks like this $\_0\_8\_$

STEP 4

Next, we need to find the remaining correct digit in the second guess, since we know that three digits are correct in their right place. The remaining correct digit is in the third place.
$\_0\_8\_$ $15673$

STEP 5

Now, we know that the second, third, and fourth digits of Noe Noe's number are0,5, and8 respectively. The number now looks like this $\_05\_8\_$

STEP 6

For the largest possible number, we should choose the largest remaining digits for the first and fifth places. The remaining digits from the two guesses are1,2,3,4,6,, and9. The largest digits are9 and.

STEP 7

Place the largest remaining digit in the first place and the second largest remaining digit in the fifth place to get the largest possible number.
$90578$ So, the largest possible number that Noe Noe could have thought of is90578.

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QuestionWhat is the largest 5-digit number Noe Noe could think of if Toe Toe's guesses 20489 and 15673 reveal 2 and 3 correct digits, respectively?

Studdy Solution

STEP 1

Assumptions1. Noe Noe's number is a5-digit number. . Toe Toe's first guess is20489 and exactly two digits are correct and in their right place.
3. Toe Toe's second guess is15673 and exactly three digits are correct and in their right place.

STEP 2

We need to find the common digits in the correct place in both guesses. These digits are0 in the second place and8 in the fourth place.
$20489$ $15673$

STEP 3

Now, we know that the second and fourth digits of Noe Noe's number are0 and8 respectively. The number now looks like this $\_0\_8\_$

STEP 4

Next, we need to find the remaining correct digit in the second guess, since we know that three digits are correct in their right place. The remaining correct digit is in the third place.
$\_0\_8\_$ $15673$

STEP 5

Now, we know that the second, third, and fourth digits of Noe Noe's number are0,5, and8 respectively. The number now looks like this $\_05\_8\_$

STEP 6

For the largest possible number, we should choose the largest remaining digits for the first and fifth places. The remaining digits from the two guesses are1,2,3,4,6,, and9. The largest digits are9 and.

STEP 7

Place the largest remaining digit in the first place and the second largest remaining digit in the fifth place to get the largest possible number.
$90578$ So, the largest possible number that Noe Noe could have thought of is90578.

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QuestionWhat is the largest 5-digit number Noe Noe could think of if Toe Toe's guesses 20489 and 15673 reveal 2 and 3 correct digits, respectively?

Studdy Solution

STEP 1

Assumptions1. Noe Noe's number is a5-digit number. . Toe Toe's first guess is20489 and exactly two digits are correct and in their right place.3. Toe Toe's second guess is15673 and exactly three digits are correct and in their right place.

STEP 2

We need to find the common digits in the correct place in both guesses. These digits are0 in the second place and8 in the fourth place.204892048920489156731567315673

STEP 3

Now, we know that the second and fourth digits of Noe Noe's number are0 and8 respectively. The number now looks like this_0_8_\_0\_8\__0_8_

STEP 4

Next, we need to find the remaining correct digit in the second guess, since we know that three digits are correct in their right place. The remaining correct digit is in the third place._0_8_\_0\_8\__0_8_156731567315673

STEP 5

Now, we know that the second, third, and fourth digits of Noe Noe's number are0,5, and8 respectively. The number now looks like this_05_8_\_05\_8\__05_8_

STEP 6

For the largest possible number, we should choose the largest remaining digits for the first and fifth places. The remaining digits from the two guesses are1,2,3,4,6,, and9. The largest digits are9 and.

STEP 7

Place the largest remaining digit in the first place and the second largest remaining digit in the fifth place to get the largest possible number.905789057890578So, the largest possible number that Noe Noe could have thought of is90578.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. Noe Noe's number is a5-digit number. . Toe Toe's first guess is20489 and exactly two digits are correct and in their right place.
3. Toe Toe's second guess is15673 and exactly three digits are correct and in their right place.

We need to find the common digits in the correct place in both guesses. These digits are0 in the second place and8 in the fourth place.
$20489$ $15673$

Now, we know that the second and fourth digits of Noe Noe's number are0 and8 respectively. The number now looks like this $\_0\_8\_$

Next, we need to find the remaining correct digit in the second guess, since we know that three digits are correct in their right place. The remaining correct digit is in the third place.
$\_0\_8\_$ $15673$

Now, we know that the second, third, and fourth digits of Noe Noe's number are0,5, and8 respectively. The number now looks like this $\_05\_8\_$

Place the largest remaining digit in the first place and the second largest remaining digit in the fifth place to get the largest possible number.
$90578$ So, the largest possible number that Noe Noe could have thought of is90578.