>> (...)However, I'm doing that because there's a
>> single position which my brother could not
>> solve, and he believes it to be impossible(...)
>>
>
> I guess you meant
>   #0#
>   #0#
> ###0###
> #######
> #######
>   ###
>   ###
>
> This indeed can not be solved. (...)

Actually, I did mean to start with:

  ###
  ###
###0###
#######
#######
  ###
  ###

and then go to:

  #0#
  #0#
#######
#######
#######
  ###
  ###

My brother's idea is that he can solve any board
after you choose the initial peg to be removed and
the first move. He can do it for any combination,
except for this one.

But your argument is very interesting, indeed!
I'll try to find that book, we'll like to read it.

Best,
Maurício

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