Answer:
A) 10
B) 39
C) the last digit must be greater than the previous digit. 0 is not greater than any other digit, so the last digit cannot be 0.
Step-by-step explanation:
A) Numbers of the form low, high, ... can start with digits 1 or 2, and the 3rd digit will be the other one. There 4 such numbers 1423, 1324, 2413, 2314. In addition, For a first digit of 2, the second digit may be 1, allowing 2143. Thus, there are 5 numbers starting with 1 or 2 and ending with 3 or 4.
There are 5 additional numbers that are the reverse of these.
There are 10 4-digit snake-like numbers containing 1–4 exactly once.
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B) We assume a "3-digit number" will be in the range 100–999. That is, the leading digit will not be zero. If you allow a leading 0, the answer is different.
With 6 as a middle digit, the numbers 1–5 can be the first digit and the numbers 0–5 can be the last digit. Hence there are 5·6 = 30 numbers of the form low-6-low.
If the form is high-6-high, there are 3 possible first digits and 3 possible last digits, so 3·3 = 9 numbers of the form high-6-high.
There are 39 3-digit snake-like numbers with 6 as the middle digit.
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C) A 7-digit snake-like number will alternate high-low, with high being the last digit. Hence the last digit must be higher than the previous digit, so cannot be 0.
