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What 5 digit number am I thinking of.

• It has two prime digits.
• Digit 3 is the highest digit.
• Digit 2 is lowest digit.
• Digit 1 is higher than the sum of digits 4 and 5.
• Digit 5 is half of digit 4.
• Digit 1 is one smaller than digit 3.
• Digit 5 is between digit 2 and digit 1
• There are no duplicates and the digit 0 doesn't appear.
Don't forget that 1 isn't prime.

The number can be represented as:

_ _ _ _ _

Since digit 5 is half of digit 4 we have four possibilities:

_ _ _ 2 1
_ _ _ 4 2
_ _ _ 6 3
_ _ _ 8 4

But since digit 1 is higher than the sum of digit 4 and digit 5 we can eliminate two possibilities leaving:

_ _ _ 2 1
_ _ _ 4 2

Since digit 5 is between digit 2 and digit 1, we can eliminate _ _ _ 2 1, leaving:

_ _ _ 4 2

Since digit 1 must be higher than the sum of digit 4 and digit 5 we have three possibilities:

7 _ _ 4 2
8 _ _ 4 2
9 _ _ 4 2

But digit 1 is 1 smaller than digit 3 we can eliminate 9 _ _ 4 2, leaving

7 _ 8 4 2
8 _ 9 4 2

Since digit 2 is the lowest number, it must be 1:

7 1 8 4 2
8 1 9 4 2

The answer has exactly 2 prime digits, which only leaves

7 1 8 4 2. QED.

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