Recover an omitted table entry from a fixed total — The Missing Piece
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Operator-authored worked example. Anchors: three mutually exclusive categories A, B and C exhaust a stated total of 100 items; A=37, B=28, C is omitted. All entries concern the same population and time, and are exact rather than rounded. Recovery: C=100-37-28=35. Check: 37+28+35=100 and all counts are nonnegative integers. Only 35 satisfies these anchors, so the numerical value is uniquely determined. Provenance: 35 is an arithmetic inference from the supplied anchors, not a retrieved original table cell, source-document excerpt or proof that an original source printed 35. Retain the anchors and derivation beside the inferred value. Non-unique contrast: if both B and C are omitted, knowing only A=37 and total=100 gives B+C=63. Both (28,35) and (30,33) satisfy it. An independent anchor such as B=28 is needed to choose a unique pair; do not invent one. Limits: overlapping categories, rounded totals, inconsistent dates or an unlisted fourth category invalidate the subtraction model. A=80 and B=30 with total=100 produces residual -10, flagging inconsistent assumptions rather than an acceptable recovered count.