What's the Name of That Book??? discussion

This topic is about
The Great Brain
SOLVED: Children's/YA
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SOLVED. Childrens about 3 brothers growing up in mid 1800s usa; think same vibe/era as Tom Sawyer but not as mischievous; kids purposefully getting sick, emergency amputations, bead belts, and the prospect of indoor plumbing. [s]
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This is one of The Great Brain series by John D. Fitzgerald, probably the first one.
Other plot details that I can't remember the whole context for include:
one boy getting am Indian (read: native american) beaded belt as a present and the other two boys trying desperately to barter him for it; indoor plumbing becoming a thing and local townsfolk being very worried as to whether or not it will make the whole house smell; and a local boy who is playing with the youngest in an abandoned barn (i think?) steps on a rusted nail and eventually his foot becomes so infected that he gets it amputated because he waited to long to tell any adults when it first happened (he would have gotten in trouble for playing in an area he wasn't supposed to).