# Twenty optional worked swaps · reveal answer after attempt

Two per day supply new finite data or a transfer question at the same target. They extend a lesson or reteach one misconception; they are not extra formal assessments. Day 5 and Day 10 swaps are **after-check** only. All numbers are invented and independently recalculated in the verifier.

| Day | Worked swap 1 · prompt → answer | Worked swap 2 · prompt → answer |
| --- | --- | --- |
| 1 | Gallery: 12 choose sculpture, 9 painting, 3 both. Distinct participants? → `12+9−3=18`; both are counted once. | App test: 10 choose text, 8 sound, 2 both. At least one? → `10+8−2=16`. |
| 2 | 14 choose sketching, 11 weaving, 20 at least one. Both? → `14+11−20=5`; if total 25, neither 5. | 9 choose puzzles, 7 music, 12 at least one. Both? → `9+7−12=4`; if total 15, neither 3. |
| 3 | Three sets 8,7,6; pairs 3,2,2; triple 1. Union? → `8+7+6−3−2−2+1=15`; each pair includes centre. | Three sets 10,9,8; pairs 4,3,3; triple 1. Union? → `10+9+8−4−3−3+1=18`. |
| 4 | One of five craft or two outdoor sessions, no shared option. Count? → `5+2=7` bookings. | One of four local or six online talks, no overlap. Count? → `4+6=10`, not 24 pairs. |
| 5 | After G: sets 8 and 7 with overlap 2, universe 17. Union/neither? → 13 in at least one and 4 neither. | After G: three indoor or two outdoor bookings, one only. Count? → `3+2=5`. |
| 6 | Four badge shapes and three captions, all pairs allowed. Count? → `4×3=12`. | Two routes and five times, every pairing allowed. Count? → `2×5=10`. |
| 7 | Branch A: 3×2; branch B: 1×4; one branch only. Count? → `6+4=10`. | Branch A: 2×4; branch B: 3×2; one branch only. Count? → `8+6=14`. |
| 8 | Seven exact regions: A only 3, B only 2, C only 1, AB only 2, AC only 1, BC only 1, all 1. Union? → 11; A=7, B=6, C=4, pair counts 3/2/2; formula returns 11. | An alleged triple count is 2 but AB pair count is 1. Possible? → No; all-three is a subset of AB, so pair must be at least 2. |
| 9 | Two-set story 11 and 8 with 3 both; a disjoint choice of 2 or 5. Methods/results? → Overlap: 16; disjoint addition: 7. | Two-stage label 3×3; exclusive branches 2×2 or 1×5. Results? → Product 9; branches `4+5=9`. |
| 10 | After H/I: sets 9,8,7; pairs 3,3,2; triple 1. Union? → `9+8+7−3−3−2+1=17`. | After H/I: exclusive routes 2×3 and 3×2. Count? → `6+6=12`; each product is a different branch. |

An instructor changes a surface context only after checking set totals, pair/triple consistency and the meaning of an outcome. Do not use a near-identical solved swap to coach a fresh check before its first response.