Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[22, 90, 23], target=180. Give (three prefix sums, is the total≤180?, target−total).
G001 — Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[22, 90, 23], target=180. Give (three prefix sums, is the total≤180?, target−total).
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Retain the ORIGINAL bank full operation prefix,domain and ordered answer roles.Use orthogonal_equal_unit only where a frame is declared,and degrees where an angle unit is declared.Integer fractions retain/1.Do not invent parameters or alter original bilingual sources.
Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap.
Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap.
Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap.
Angle ORIGINAL target minus total := sub(180, 135)
After
Angle ORIGINAL target minus total = 45
Conditions: none
Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap.
The flag tests total<=180,NOT total<=target.With target90,total100 may have flagYes and remainder-10.Each raw part is within0..180;an accumulated540 is legal arithmetic but not an angle in this entry.Keep original prefix order without sorting/wrapping.
S006 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
S005 · premise_and_result_audit — Recompute Angle ORIGINAL target minus total with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Recompute Angle ORIGINAL ordered prefix2 with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Angle ORIGINAL ordered prefix1 with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute Angle ORIGINAL ordered prefix0 with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
Result
([22, 112, 135], Yes, 45)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.