Selia is an international spy trying to crack a coded message. The message contains a 5 digit number that will open a lock box that holds the contents wanted by every top villain in the world. Use the following clues to help Selia crack the code. You only get one chance or the lock box will self destruct. Good luck!
*The number consists of 3 different digits.
*All digits are odd numbers.
*The value of the hundreds digit is 10 times as much as the value of the tens digit.
*The digit in the hundredths place is a multiple of the digit in the tens place.
*The digit in the tenths place is 1/10 of the value of the digit in the ones place.
*The sum of the digits in the ones and tenths place is one more than the digit in the hundredths place.
Part A
What is the 5 digit number?
Part B
Explain how you know that the number you chose is the only 5 digit number that fits al of the clues.
"...hundreds digit is 10 times as much as the value of the tens..."
If that is true, the hundreds digit can NOT be an odd number
Ten times any old digit is even. Moreover 10 times any digit is no longer a single digit.
51.9
Part A:
Alright, let's break down the clues one by one to find the 5-digit number:
1. The number consists of 3 different digits.
2. All digits are odd numbers.
So, we know that our number will have three different odd digits.
3. The value of the hundreds digit is 10 times as much as the value of the tens digit.
This means that our hundreds digit will have to be ten times greater than the tens digit. Since all the digits are odd, the only combination that works is 9 and 1. So, we have 91XXX.
4. The digit in the hundredths place is a multiple of the digit in the tens place.
Since the tens digit is 1, the hundredths digit must be a multiple of 1, which means it can also be 1. Our current number is 911XX.
5. The digit in the tenths place is 1/10 of the value of the digit in the ones place.
The ones digit can only be 3, 5, 7, or 9. So the tenths digit, being 1/10 of the ones digit, can only be 0.1, 0.5, 0.7, or 0.9. But since we are working with digits, it can only be 1. Thus, our number becomes 9111X.
6. The sum of the digits in the ones and tenths place is one more than the digit in the hundredths place.
The digit in the hundredths place can only be 1 (as we found in clue 4), so the sum of the ones and tenths digits must be 2. Only one combination works: 1 + 1 = 2. Our final number is 91112.
Part B:
The number we chose, 91112, is the only 5-digit number that fits all the clues. We went step by step, following each clue to determine the specific values for each digit. By using deduction and applying the constraints given, we arrived at a unique solution that satisfied all the given conditions.
Part A:
To solve this puzzle and find the 5-digit number, let's consider the given clues one by one.
1. The number consists of 3 different digits.
Since all three digits are odd, we have five options to choose from for each digit: 1, 3, 5, 7, or 9.
2. The value of the hundreds digit is 10 times as much as the value of the tens digit.
This means that the hundreds digit must be 10 times one of the possible values for the tens digit. We can determine the possible pairs by multiplying each possible value for the tens digit by 10, as follows:
Tens digit: 1, Hundreds digit: 10
Tens digit: 3, Hundreds digit: 30
Tens digit: 5, Hundreds digit: 50
Tens digit: 7, Hundreds digit: 70
Tens digit: 9, Hundreds digit: 90
3. The digit in the hundredths place is a multiple of the digit in the tens place.
Since the tens digit is an odd number, the only possible odd multiples are 1 and the number itself. We can now narrow down the options based on the previously calculated pairs:
Pair: 1, Hundredths digit: 10 or 100
Pair: 3, Hundredths digit: 30
Pair: 5, Hundredths digit: 50
Pair: 7, Hundredths digit: 70
Pair: 9, Hundredths digit: 90
4. The digit in the tenths place is 1/10 of the value of the digit in the ones place.
Since the ones place must be an odd number, the tenths place can only be 0.1, 0.3, 0.5, 0.7, or 0.9, and thus, the tenths place cannot be an odd number. Therefore, none of the options we have considered so far are valid.
5. The sum of the digits in the ones and tenths place is one more than the digit in the hundredths place.
Considering the previous clues, we know that the ones place and tenths place are both even (0.1, 0.3, 0.5, 0.7, or 0.9), and therefore their sum cannot be odd. Since the digit in the hundredths place is odd, this clue cannot be satisfied.
Based on these clues, it seems there is no possible 5-digit number that fits all of the given conditions. Selia will need to reexamine the code or seek additional clues.
Part B:
We can conclude that there is no valid 5-digit number that satisfies all the given clues. This can be determined by carefully analyzing each condition and ruling out the possibilities step by step. In this case, we were able to identify a contradiction in the requirements, specifically in clue number 4, where the tenths place being an odd number conflicted with the other clues.
By thoroughly understanding and evaluating each clue, we can confidently assert that no valid solution exists. It is important to carefully consider all the information provided and make logical deductions to reach a conclusion.