Even Digits Are Different Puzzle - Solution
The Puzzle:
I am a 3-digit number.
All my digits are even, and they are all different.
The sum of my digits is 12.
My tens digit is larger than my hundreds digit.
If you reverse my digits, the new number is 198 less than the original.
What number am I?
Our Solution:
Even digits are 0, 2, 4, 6, 8. Since it's a 3-digit number, the hundreds digit cannot be 0.
Sum is 12: Possible combinations (hundreds, tens, units):
(2, 4, 6) ⇒ Sum = 12
(2, 6, 4) ⇒ Sum = 12
(4, 0, 8) ⇒ Sum = 12
(4, 2, 6) ⇒ Sum = 12
(6, 2, 4) ⇒ Sum = 12
(8, 0, 4) ⇒ Sum = 12
My tens digit is larger than my hundreds digit.
(2, 4, 6) ⇒ 4 > 2 Yes
(2, 6, 4) ⇒ 6 > 2 Yes
(4, 0, 8) ⇒ 2 > 4 No
(4, 2, 6) ⇒ 2 > 4 No
(6, 2, 4) ⇒ 2 > 6 No
(8, 0, 4) ⇒ 0 > 8 No
Possible candidates: 246 and 264
Reversed number is 198 less than original:
For 246: Reversed = 642 ⇒ 642 - 246 = 396 (Not 198)
For 264: Reversed = 462 ⇒ 462 - 264 = 198 Yes
The number is 264.