Solve the mathematical puzzle.
Determine the digits of Z from these clues.
The fourth digit of Z is the largest prime factor of 35.
The first digit of Z is the smallest prime factor of 24, other than 1.
The last digit of Z plus the third digit of Z add to 12.
The second digit of Z is the largest prime factor of 6.
Z is a four-digit number.
2,357
Let's solve the puzzle step by step:
Step 1: The fourth digit of Z is the largest prime factor of 35.
The prime factors of 35 are 5 and 7. Since 7 is the largest prime factor, the fourth digit of Z is 7.
Step 2: The first digit of Z is the smallest prime factor of 24, other than 1.
The prime factors of 24 are 2, 2, 2, and 3. The smallest prime factor, other than 1, is 2. So, the first digit of Z is 2.
Step 3: The last digit of Z plus the third digit of Z add to 12.
Let's denote the last digit of Z as a and the third digit as b. According to the given clue, a + b = 12.
Step 4: The second digit of Z is the largest prime factor of 6.
The prime factors of 6 are 2 and 3. Since 3 is the largest prime factor, the second digit of Z is 3.
Step 5: Z is a four-digit number.
Since Z is a four-digit number, and we already determined the first three digits, let's denote the last digit as c.
Step 6: Putting all the digits together, we have Z = 2 _ 3 7, where _ represents the unknown digit.
Step 7: Using the clue from Step 3, we have c + 3 = 12. Solving for c, we get c = 9.
Step 8: Putting all the digits together, the solution for Z is Z = 2 9 3 7.
So, the digits of Z are 2, 9, 3, and 7.
To solve this mathematical puzzle and determine the digits of Z, we will break down each clue one by one.
Clue 1: The fourth digit of Z is the largest prime factor of 35.
The prime factors of 35 are 5 and 7. Since 7 is the larger of the two, we know that the fourth digit of Z is 7.
Clue 2: The first digit of Z is the smallest prime factor of 24, other than 1.
The prime factors of 24 are 2, 2, and 3. The smallest prime factor, other than 1, is 2. Thus, the first digit of Z is 2.
Clue 3: The last digit of Z plus the third digit of Z add to 12.
From this clue, we know that the sum of the last and third digit equals 12. Let's call the last digit L and the third digit T. So, L + T = 12.
Clue 4: The second digit of Z is the largest prime factor of 6.
The prime factors of 6 are 2 and 3. The largest prime factor is 3, so the second digit of Z is 3.
From these clues, we can now construct the four-digit number Z.
The second digit is 3.
The first digit is 2.
The third digit plus the last digit is 12.
We can try different combinations for the third and last digits that satisfy this condition, such as 9 and 3 or 8 and 4.
If we choose the third digit as 9 and the last digit as 3, we have the number 2937.
If we choose the third digit as 8 and the last digit as 4, we have the number 2834.
So, there are two possible four-digit numbers that satisfy the given clues: 2937 and 2834.
Damon did one of these for you.
See what you can do with this one.