There are words from which you can remove a "chunk", leaving a new word. Like this:

    WISHBONE

WI SHBO NE

WI   SHBO   NE

WI   <poof!>  NE

WI            NE

WI     NE

WINE


There are also words that work the other way, for which inserting a "chunk" produces a new word. For example, you can insert the chunk AUTIFI into the word BEER to make BEAUTIFIER.

A "chunk" is a string of consecutive letters. It must consist of at least two letters (no single-letter chunks). It does not need to be a valid English word.

Now, what if I told you there are words from which you can remove a chunk, then insert a different chunk with different letters, and get the original word again?

What the heck am I talking about?!

There are actually thousands of such examples. I'm just looking for a general description of the pattern that creates this strange phenomenon.

(Too easy? Too hard? Try the counterpart subtraction paradox.)

Afterword:

Here is the specific example which motivated this post:

Start with the word QUARTERBACK and remove the chunk RTERBA to obtain QUACK. Now, take the new chunk ARTERB (which is obviously different from the chunk that was removed) and insert it into the word QUACK to obtain the original word QUARTERBACK again.

Perfectly identical, but not exactly the same! It's a little bit of a shell game, and if you followed it with sharp eyes, you might have noticed that it was the first "A" in QUARTERBACK which was retained in QUACK, but then it became the second "A" when QUARTERBACK was restored.

The two "A" are like sentinels which stand on either side of a middle string of letters. The chunk which is removed must contain the middle string of letters as well as one of the sentinels. The chunk which is inserted must contain the middle string of letters as well as the other sentinel.

@GarethMcCaughan did a good job below of exploring whether the sentinels can be more than a single letter. They can be!

• In both your afterword and in Gareth McCaughan's answer, impressive solutions with a 6-letters chunks are offered. I wonder if this is the maximum, so I am gonna create a new question asking for the longest possible chunk. Jul 19 '19 at 7:59
• @Evargalo — Right on! Jul 19 '19 at 13:40

I assume that

"with different letters" means only that the sequence of letters isn't the same, rather than that the (multi)set of letters isn't, because otherwise the thing seems to be genuinely impossible unless there's some sort of lateral-thinking nonsense going on.

In that case

D(ESP)ERATE can lose ESP to make DERATE and then gain SPE to make DE(SPE)RATE again. Or R(ESIGN)ED can lose ESIGN to make RED and then gain SIGNE to make RE(SIGNE)D again.

The general picture here is

that you have words ABCBD and ABD where A,B,C,D are arbitrary strings of letters. The easiest cases (as above) have B a single letter, but I bet there are some where B is longer. At any rate, you're then removing BC and inserting CB or vice versa.

Yes, B can certainly be longer. For instance, BANYANS can lose ANY and gain YAN or vice versa. Or consider HONEYMOONED; you can lose ONEYMO making HONED and then gain YMOONE to get HONEYMOONED again.

• Thank you for your clarification. Yes, I only meant that the sequence of letters isn't the same, not the set of letters used. (It would be truly magical to remove a chunk containing a letter "J", then insert a chunk that does not contain any "J" and expect to get the same original word back again, wouldn't it?) The phrasing was studiously nonspecific to avoid giving any unintentional hints. Jul 17 '19 at 15:36

Are you talking about...

words that have the pattern "...X(...X)...", where X is any letter and () marks the chunk to remove? For example, you can take NIN out of FANNING to get FANG, then add NNI into the middle of it to getFANNING$$`$$ again.

One suggestion

From

DECENT

You can remove the chunk

EC

and get

DENT

But if now you had the different chunk

CE

You can come back to the first word,

DECENT

• Creative! (+1) :P Jul 17 '19 at 19:50

Here is one

HANDSOME, from which you can remove ANDS to get HOME

and

add jumbled SAND to HOME to get HANDSOME again.

Few more are:

M(ORE)OVER, B(RACEL)ET

• Is it allowed to jumble the chunk you add ? Jul 18 '19 at 7:33
• @Evargalo - no, as per the OP. However, chunk of the OP allows that but not different chunk. Jul 18 '19 at 8:38

From

FAVOUR

you can remove

VOU to get FAR

VO to get FAVOR

which is the same word, but a different spelling.

I'm pretty sure it's easy to understand what the OP is talking about if you've tried to solve this question before. :)

Solution:

If the word is [Left][Old chunk][Right], the new chunk must be added from somewhere else, splitting the left or right part into two. Let's say it consists of five parts, as in [I][II][Old chunk][III][IV] (I or IV can be empty):

If [I][II][Old chunk][III][IV] = [I][New chunk][II][III][IV],
[II][Old chunk] = [New chunk][II] ([Old chunk] is made up of [V][II], [New chunk] of [II][V])
Our word would be [I][II][V][II][III][IV].

If [I][II][Old chunk][III][IV] = [I][II][III][New chunk][IV],
[Old chunk][III] = [III][New chunk] ([Old chunk] is made up of [III][V], [New chunk] [V][III])
Our word would be [I][II][III][V][III][IV].

• Ha, thanks for noticing! Yes, these "paradoxical" observations came out of my work on that river-crossing puzzle. Jul 17 '19 at 21:42