Let's solve the secret code step-by-step using the given clues:
1. The digit in the ten thousands place is 5.
- So, the ten thousands place (D5) = 5
2. The digit in the thousands place is twice the digit in the hundred thousands place.
- Let the thousands place be D4 and hundred thousands place be D6.
- So, D4 = 2 D6
3. The digit in the ones place is 2 more than the digit in the millions place.
- Let the ones place be D7 and millions place be D1.
- So, D7 = D1 + 2
4. The digit in the millions place is 8 less than the digit in the hundreds place.
- Let the hundreds place be D3.
- So, D1 = D3 - 8
5. The digit in the millions place is 1 less than the digit in the tens place.
- Let the tens place be D2.
- So, D1 = D2 - 1
To sum up, we must find seven distinct digits fitting the following equations:
- D5 = 5
- D4 = 2 D6
- D7 = D1 + 2
- D1 = D3 - 8
- D1 = D2 - 1
Now, we'll substitute D1:
1. From D1 = D2 - 1, we have:
- D2 = D1 + 1
2. From D1 = D3 - 8, we have:
- D3 = D1 + 8
Let's find possible values satisfying all conditions. We should choose an integer for D1 such that all other digits (within their typical range of 0-9) remain distinct and meet the equations:
### Step-by-step:
- D1 = Millions Place:
- Must be a digit such that D1 + 8 and D1 + 1 are also digits (all from 0-9).
- Let's start by testing values.
Check potential values for D1 (from 0 to 9):
- If D1 = 1:
- D2 = D1 + 1 = 2
- D3 = D1 + 8 = 9
- D7 = D1 + 2 = 3
- We now have: Millions (D1) = 1, Tens (D2) = 2, Hundreds (D3) = 9, Ones (D7) = 3.
With these values, D4 = 2 D6 must be checked to ensure all unique digits and proper domain challenge:
- We have digits used so far: {1, 2, 3, 5, 9}. Potential digits left {0, 4, 6, 7, 8}.
- If D6 = 4, then D4 = 24 = 8 fits into digital free zeros.
Thus, another context values for full check:
- D1 = 1
- D2 = 2
- D3 = 9
- D4 = 8
- D5 = 5
- D6 = 4
- D7 = 3
These digits {1, 2, 3, 4, 5, 8, 9} are different and fit all given constraints.
Thus, the correct 7-digit secret code for the safe is: 1295853
