Solutions to the Exercises

Chapter 0 — What a Wohngeldbehörde Decides, and Why It Is a Law-as-Code Problem

1. Not enough facts — the amount is not established. Without the rent, the formula has no M, so there is no amount to compute; returning €0 would state that the family is owed nothing, which nobody has decided.
2. The monthly Wohngeld depends on the date (€463 on 31 December 2024, €485 on 1 January 2025). In this case the income (€1,710.00) and the rent taken into account (€777.80) are the same on both dates; Chapter 2 shows why.
3. The claim needs more than the formula: the amount must be at least €10 (§ 21 Nr. 1), not all members may be excluded (§ 21 Nr. 2), and claiming must not be abusive — an assessment the model leaves to the Wohngeldbehörde (§ 21 Nr. 3). Chapter 6 shows what happens when that assessment is still missing.

Chapter 1 — Which Text Applies? The Bundesgesetzblatt and the § 44 Transition

1. It must decide again, of its own motion, for 1 January to 30 September 2025, applying the values of the second WoGFV: €463 a month until 31 December 2024 and €485 a month from 1 January 2025.
2. It returns no amount, with the issue MISSING_PARAMETER_VALUE. A carried-over value would look like a lawful amount without saying which text it rests on; the refusal names what is missing — the values for the new period.
3. In Munich the rent (€1,225) is above the ceiling, so the ceiling decides the rent taken into account, and the ceiling rose. In Weimar the rent (€580) stays under the ceiling on both days, so the rent itself is used: €580 + €197.80 = €777.80 in both editions.

Chapter 2 — Household, Rent and Income

1. €26,880 − €2,000 = €24,880; minus 20 % = €19,904 a year; Y = €19,904 ÷ 12 = €1,658.6666666667 — the model holds Y at ten decimal places (rounded half up), not rounded to the cent — and the Wohngeld becomes €499. Proven expenses replace the flat rate only when they are higher, as here.
2. The rent (€850) is now above the ceiling plus the climate component (€800.40), so the ceiling counts: M = €800.40 + €197.80 = €998.20, and the Wohngeld becomes €644.
3. Because § 5 Abs. 1 makes membership depend on facts — the centre of one’s life, the relationship to a member — not on registration. The case must establish those facts: a person whose life centre in the flat is not established is not counted (section 6), and a person whose status under § 7 is unknown leaves the household not established (Chapter 8).

Chapter 3 — One Family, One Decision: Weimar, Mietenstufe III, €485

1. The place of residence — wohnort — because the rent level is read from the WoGV’s list for the municipality (§ 12 Abs. 1 WoGG with the Anlage to § 1 Abs. 3 WoGV). The case has no field for the level; it follows from the place.
2. § 11 Abs. 1 WoGG: the rent counts only up to the ceiling of Anlage 1 (§ 12 Abs. 1) plus the climate component (§ 12 Abs. 7) — €800.40 for four members at level III in 2025.
3. The assertion behoerde-21-nr3 with origin adjudicated: the Wohngeldbehörde has assessed that claiming would not be abusive. Without it, the claim would require judgment.

Chapter 4 — The § 19 Formula: Anlagen 2 and 3 and One Rounding

1. With the values of 31 December 2024:

   z1 = 0.01 + 0.0002251 · 777.80 + 0.00002 · 1,710
      = 0.01 + 0.17508278 + 0.0342
      = 0.2192827800

   The remaining steps give z2 = 374.9735538000, z3 = 402.8264462000, z4 = 463.2504131300, and €463.

2. Because Anlage 3 Nr. 2 prescribes ten decimal places for the intermediate steps and Nr. 3 allows rounding to the euro only at the end. Rounding earlier is a different calculation and can change the amount by a euro.

3. When z4 lies very close to a half euro, so that the small differences between rounding and cutting off at the tenth decimal place — carried through z2 and z4 — put it on different sides of the 50-cent line.

Chapter 5 — How a Scenario Is Written

1. An expectation copied from the engine only checks that the engine agrees with itself. The PDF is an independent statement of the answer; agreement with it is evidence.
2. Two errors that cancel out — for example a wrong ceiling and a wrong heating relief that happen to give the right total — or the right total reached through the wrong path.
3. No. They are owner-occupier subsidies (Lastenzuschuss), which the model declares outside its scope; for them it returns a flag, not an amount. The scope line — 18 of 21 executed — says so openly.

Chapter 6 — Sum Known, Claim Pending: § 21 Nr. 3 and the Wohngeldbehörde

1. Only the claim. The income, the rent and the amount stay established; the claim to €485 becomes not established, and “no claim, ground § 21 Nr. 3” becomes established.
2. Because the model leaves that assessment to the Wohngeldbehörde. Treating silence as “not abusive” would turn the office’s decision into a default of the software; the household would receive a claim nobody competent has confirmed.
3. A threshold. § 21 Nr. 3 names “considerable assets” only as an example and sets no amount; a fixed limit would replace the office’s assessment with a number the Act does not contain. If an authority adopts internal guidance with a threshold, that guidance is a separate source and must be named as such.

Chapter 7 — Excluded by Another Authority’s Decision: § 7 WoGG

1. The exclusion no longer applies (§ 7 Abs. 1 S. 3 Nr. 1): she is a counted member, and the model computes Wohngeld for her household, provided the other facts are complete.
2. Because § 7 Abs. 1 excludes recipients only “wenn bei deren Berechnung Kosten der Unterkunft berücksichtigt worden sind”. Receiving the benefit without housing costs does not exclude.
3. Because § 7 excludes person by person: the son receives SGB II support with housing costs, the father does not. So not all members are excluded (§ 21 Nr. 2 does not apply), and the household’s Wohngeld is computed for the one counted member, with the rent taken in proportion under § 11 Abs. 3. (Had the excluded son been the applicant, § 3 Abs. 4 would have kept him entitled to claim for the household.)

Chapter 8 — Missing Facts, Conflicting Records and the Model’s Boundary

1. The income (€1,710.00) and the rent level (Mietenstufe III, from the place). Not the rent taken into account, and so not the amount.
2. Because the most recent record is not necessarily the correct one. BOTH keeps both records and their sources and leaves the resolution to the person who can check them; a silent choice would hide the conflict in the decision.
3. “Outside the model” says the model does not cover owner-occupier subsidies; it says nothing about her entitlement. She may well be entitled to a Lastenzuschuss. The office must decide her case by other means.

Chapter 9 — Audit and Reproduction

1. The same rules and parameters were evaluated, on different facts or a different date. Here: Familie2025 and Familie20241231 differ only in the date, which selects other rows of the annexes.
2. The program (was the bundle replayed with a different program or language version — compare the semantics and program fingerprints in the manifest) and the inputs (was the saved bundle changed — compare the case fingerprint).
3. Replay shows that the computation is reproducible. It does not show that the rules read the Act correctly or that the facts were true; those need a legal review and the file.