Discussion
A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?
Answer: D
There are 80 frabjous numbers.
The odd digits are 1, 3, 5, 7, 9. The first digit can be any of the 5. Each later digit must be odd and differ from the digit just before it, leaving 4 choices:
\[ 5 \times 4 \times 4 = 80 \]
Only adjacent digits must differ, so the first and third may be equal (as in 131). 125 = 53 ignores the 'no two adjacent equal' rule, and 60 = 5 × 4 × 3 wrongly forbids repeats of non-adjacent digits as well.
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