One technique to make a high pass filter is to subtract a lowpass filter from a wire (meaning subtract the output of the filter from the input as I have demonstrated in this post).
What lowpass can you subtract from a wire that will result in an all-pass? Specifically pass all frequencies with unity gain and modify the phase only, such that the group delay is 1 sample?
This is a “DSP Puzzle”, please preface your answer with spoiler notation by typing ythe following two characters first ">!"