The Assumption Method

1. 1The Gap Becomes Empty SlotsAn all-chicken flock has only 40 legs, but the farm really has 56. The missing 16 legs appear as 16 dashed empty slots — holes waiting to be filled.56 − 40 = 16 legs missing
2. 2Look Closely at the First OneWe zoom in on the first chicken to measure one swap very slowly. A rabbit has 4 legs, a chicken has 2 — make your guess before the swap.4 legs (rabbit) ↔ 2 legs (chicken)
3. 3Measure One SwapThe chicken turns into a rabbit: two gold legs grow into exactly the first two slots, and the counter ticks up by exactly 2 legs.4 − 2 = 2 legs per swap
4. 4Swap the Rest, FasterSame rhythm, faster: each swap turns one more chicken into a rabbit and fills two more slots gold. The counter climbs to 56 legs.40 → 56 legs
5. 5Assemble the Formula from EvidenceThe number 16 flies up from the filled slot row; the number 2 flies up from the very gold legs of the measured swap. Dividing the gap by the gain per swap gives the number of swaps.16 ÷ 2 = 8 rabbits
6. 6Find the ChickensThe number 20 flies down from the herd label, the number 8 from the answer just assembled. The rest of the herd are chickens.20 − 8 = 12 chickens
7. 7Check on the HerdRecount right on the herd: sweep the rabbit legs first — 4 per rabbit — then the chicken legs, 2 each. The total matches the 56 legs in the problem.8 × 4 + 12 × 2 = 56
8. 8The Summary CardThree lines sum up the whole method: assume — the gap — the number of swaps. The final herd has 8 rabbits and 12 chickens.16 ÷ 2 = 8 swaps
9. 9The AnswerThe opening question is answered: assuming all chickens leaves us 16 legs short, and each swap gains 2. The farm has 8 rabbits and 12 chickens.8 rabbits + 12 chickens = 20 animals

Change the numbers and watch the diagram redraw itself: