THE BROKEN CLOCK PUZZLE

Michael is a handy guy who makes things.  He makes ukuleles, tooling, jigs, furnishings, displays, takes photos, and so on.  While he is active in many kinds of such projects, the people who use them generally agree that Michael’s stuff is much better than it looks or functions, despite how overpriced it all is.

Michael recently made a wall clock out of scraps, cutoffs, and leftovers of various materials.  It worked fine . . . until a particularly volatile series of anti-government rants by Bob knocked it off the wall.  The clock hit the floor, just missing Denyse and Carol-#1-the-taller, and broke into three pieces.  They, being used to Bob’s rants, continued chatting.

  Sarah A. jumped out of her seat in fright, fearing a ninja assassination attempt in progress.   Sara S. emitted a shriek so high-pitched that only the dogs could hear it; every cup and glass in the room shattered.   Carol-#2-the-shorter, in an unexpected manifestation of fight-or-flight syndrome, was reduced to the only-recently-discovered third reaction: helpless giggles and hiccups.  Jamie clung to both her doggie and Liz with an alacrity heretofore unseen, leaving indentations in them that would last the rest of the day.  Ervin was . . . well, it was hard to tell.  He might have had a hangover or was experiencing flashbacks.  You never know, with him.

Just as Michael and Trini were about to clean the mess up, Barbara walked in.

She took one look at the broken clock and — in a breathless utterance delivered with Laurence-Olivier-like composure and accompanying British accent said: “OH MY GOD, MICHAEL.  LOOK!   THE CLOCK BROKE INTO THREE PIECES IN SUCH A WAY THAT THE NUMBERS ON EACH CHUNK ADD UP TO THE SAME TOTAL!” 

 HOW DID THE CLOCK BREAK?  WHAT NUMBERS FROM ONE TO TWELVE DID EACH PIECE CONTAIN?