The digits from 1 to 9 can be arranged in a row, such that any two neighbouring digits in this row is the product of two one-digit numbers. Arrangement:
$$728163549$$
Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F? Here the row has 15 digits and all numbers are treated as hexadecimal numbers. Example: 123456789ABCDEF 12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.
Answer
One solution is
$$D2379A5B6C4E18F$$
Thought process:
No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.
The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$
Therefore we must have subsequences $E1$ and $D2$. From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$
No comments:
Post a Comment