Think of a five-digit number composed of odd numbers. The thousands digit is two less than the ten thousands digit but two more than the hundreds digit. The tens digit is two more than ones digit which is four less than the hundreds digit?

Question

Think of a five-digit number composed of odd numbers. The thousands digit is two less than the ten thousands digit but two more than the hundreds digit. The tens digit is two more than ones digit which is four less than the hundreds digit?

Answer 1

If the digits, reading left to right, are abcde, then we are told

b = a-2
b = c+2
So, abc are consecutive descending odd numbers.
d = e+2
e = c-4
Looks like all 5 digits are in order:

97531

Answer 2

To solve this problem, let's break down the given clues step by step:

1. The thousands digit is two less than the ten thousands digit but two more than the hundreds digit.

Let's assign variables to the thousands, ten thousands, and hundreds digits:
- Ten thousands digit = T
- Thousands digit = Th
- Hundreds digit = H

According to the given clue, we can write the equation as:
Th = T - 2
Th = H + 2

2. The tens digit is two more than the ones digit, which is four less than the hundreds digit.

Let's assign variables to the tens and ones digits:
- Tens digit = Te
- Ones digit = O

According to the given clue, we can write the equation as:
Te = O + 2
O = H - 4

Now we have a system of equations based on the given clues. To find the five-digit number composed of odd numbers, we need to find values for T, Th, H, Te, and O.

Let's solve the system of equations:

1. From the first clue:
Th = T - 2 ... (Equation 1)
Th = H + 2 ... (Equation 2)

Substituting Equation 2 into Equation 1, we get:
H + 2 = T - 2
H = T - 4 ... (Equation 3)

2. From the second clue:
Te = O + 2 ... (Equation 4)
O = H - 4 ... (Equation 5)

Substituting Equation 5 into Equation 4, we get:
Te = H - 2 ... (Equation 6)

Now we have three equations (Equations 3, 5, and 6) with three variables (H, T, and Te). By solving this system of equations, we can find the values for H, T, and Te.

Let's solve this system algebraically:

From Equation 3:
H = T - 4

Substituting this value of H into Equation 5:
O = (T - 4) - 4
O = T - 8

Now, let's substitute these values of H and O into Equation 6:
Te = (T - 4) - 2
Te = T - 6

So, we have the following relationships:
- H = T - 4
- O = T - 8
- Te = T - 6

Since we are looking for a five-digit number composed of odd numbers, we know that all the variables (T, Th, H, Te, and O) must be odd numbers. However, there is no solution to this system of equations with all odd numbers.

Hence, the given clues do not lead to a valid five-digit number composed of odd numbers.