QuestionFind the largest 5-digit number Noe Noe could think of, given Toe Toe's guesses: 20489 (2 correct) and 15673 (3 correct).
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.
4. We need to find the largest possible number that Noe Noe could have thought of.
STEP 2
Let's start by analyzing the first guess. We know that two digits are correct and in their right place. These digits could be any two out of the five digits in the guess20489.
STEP 3
Now, let's analyze the second guess. We know that three digits are correct and in their right place. These digits could be any three out of the five digits in the guess15673.
STEP 4
We need to find the common digits that are in the correct place in both guesses. These digits will definitely be in the final number.
STEP 5
The common digits in the correct place in both guesses are1 and8. So, the first and fourth digits of Noe Noe's number are1 and8 respectively.
STEP 6
Now, we need to find the third digit of Noe Noe's number. This digit is correct in the second guess but not in the first guess. So, the third digit of Noe Noe's number is6.
STEP 7
The remaining two digits are the second and fifth digits of Noe Noe's number. These digits are not correct in either guess. Since we want to find the largest possible number, we should choose the largest possible digits for these positions.
STEP 8
The largest possible digit for the second position is (since it is not used yet), and the largest possible digit for the fifth position is7 (since it is not used yet and is already used).
STEP 9
So, the largest possible number that Noe Noe could have thought of is19687.
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