think of a five digit number composed of odd numbers. the thousands digits is two less than the ten thousands digit but two more than the hundreds digit. the tens digits is two more that ones digit which is less than the hundreds digit.
97553
97531
75331
97531
To find the five-digit number with the given conditions, we can follow these steps:
Step 1: Start with the thousands digit: The thousands digit is two less than the ten thousands digit but two more than the hundreds digit. Let's represent the ten thousands digit as A, the thousands digit as B, and the hundreds digit as C. From the given conditions, we can form the equation:
B = A - 2
B = C + 2
Step 2: Move on to the tens digit: The tens digit is two more than the ones digit, which is less than the hundreds digit. Let's represent the tens digit as D and the ones digit as E. From the condition, we can create the equation:
D = E + 2
E < C
Step 3: Consider the number pattern: Since we need a five-digit number composed of odd numbers, the ten thousands digit (A) must be odd.
Step 4: Combine the equations and determine the range: Now, let's consider the range for each digit to satisfy the given conditions:
- A (ten thousands digit): An odd number, so it could be 1, 3, 5, 7, or 9.
- B (thousands digit): B = A - 2, so B could be A - 2 from the selected values for A.
- C (hundreds digit): B = C + 2, so C = B - 2 from the selected values for B.
- D (tens digit): D = E + 2, so D could be E + 2 from the selected values for E.
- E (ones digit): Less than C, so E could be any odd number less than C.
Step 5: Test the values: Iterate through the possible values and check if they meet the given conditions.
The possible values satisfying the conditions are as follows:
- A = 3, B = 1 (3 - 2), C = -1 (1 - 2), D = -1 (E + 2), E = -3
- A = 7, B = 5 (7 - 2), C = 3 (5 - 2), D = 1 (E + 2), E = -1
- A = 9, B = 7 (9 - 2), C = 5 (7 - 2), D = 3 (E + 2), E = 1
Since we need a positive value for each digit, the only valid combination is:
A = 9, B = 7, C = 5, D = 3, E = 1
Therefore, the five-digit number composed of odd numbers that satisfies the given conditions is 97531.