Can you arrange ABCD...Z into a straight line so that consecutive letters of the alphabet have an odd number of letters between them?

Question

Can you arrange the 26 letters of the English alphabet (ABCD...Z) into a straight line so that consecutive letters of the alphabet have an odd number of letters between them? You must use each letter exactly once.

Examples:

Having XCY somewhere in the line is okay for X and Y because there is one letter between them.

Having XCMY somewhere in the line is not okay for X and Y because there are two letters between them.

Having YPAQX somewhere in the line is okay for X and Y because there are three letters between them. And it is also fine for P and Q.

Answer 1

Consider all 26 positions a letter can be in, then give each of them a parity. (The first is odd, the second even, third odd and so on until the twenty-sixth is even.)
Put a letter A in any position. Then, consider what parity the letter B will have. Since it must have an odd number of letters between it and A, the position it is on must share the same parity as A.

From this, we can see that any two consecutive letters must have the same parity. However, since all the consecutive letters of the alphabet form a single chain, all 26 letters must have the same parity, and this is impossible, as there are only 13 slots available for either parity.
Thus, the task is impossible.

Answer 2

TakingNotes is correct

if you use only letters from the english alphabet it is not possible as all positions must have the same parity (even/odd)

but thinking outside the box

you could place all english letters in an odd position (or all in an even position if you like) and fill the gaps with letters from other alphabets (Greek, Cyrillic, German umlauts, ...)