========================== Plan Near with 5 plants ========================== Where Cum. steps Water amt. Cum. step-units --------- ---------- ---------- --------------- Plant 1 1 3 3 Plant 2 2 2 5 Plant 3 3 1 6 FAUCET 6 0 6 Plant 4 10 3 18 Plant 5 11 2 20 FAUCET 16 1 25 Plan Near: Total steps = 16, total step-units = 25 ========================= Plan Far with 5 plants ========================= Where Cum. steps Water amt. Cum. step-units --------- ---------- ---------- --------------- Plant 5 5 3 15 Plant 4 6 2 17 Plant 3 7 1 18 FAUCET 10 0 18 Plant 2 12 3 24 Plant 1 13 2 26 FAUCET 14 1 27 Plan Far: Total steps = 14, total step-units = 27 *** With 5 plants, Plan Near is better with 2 fewer step-units. ========================== Plan Near with 6 plants ========================== Where Cum. steps Water amt. Cum. step-units --------- ---------- ---------- --------------- Plant 1 1 3 3 Plant 2 2 2 5 Plant 3 3 1 6 FAUCET 6 0 6 Plant 4 10 3 18 Plant 5 11 2 20 Plant 6 12 1 21 FAUCET 18 0 21 Plan Near: Total steps = 18, total step-units = 21 ========================= Plan Far with 6 plants ========================= Where Cum. steps Water amt. Cum. step-units --------- ---------- ---------- --------------- Plant 6 6 3 18 Plant 5 7 2 20 Plant 4 8 1 21 FAUCET 12 0 21 Plant 3 15 3 30 Plant 2 16 2 32 Plant 1 17 1 33 FAUCET 18 0 33 Plan Far: Total steps = 18, total step-units = 33 *** With 6 plants, Plan Near is better with 12 fewer step-units. ========================== Plan Near with 7 plants ========================== Where Cum. steps Water amt. Cum. step-units --------- ---------- ---------- --------------- Plant 1 1 3 3 Plant 2 2 2 5 Plant 3 3 1 6 FAUCET 6 0 6 Plant 4 10 3 18 Plant 5 11 2 20 Plant 6 12 1 21 FAUCET 18 0 21 Plant 7 25 3 42 FAUCET 32 2 56 Plan Near: Total steps = 32, total step-units = 56 ========================= Plan Far with 7 plants ========================= Where Cum. steps Water amt. Cum. step-units --------- ---------- ---------- --------------- Plant 7 7 3 21 Plant 6 8 2 23 Plant 5 9 1 24 FAUCET 14 0 24 Plant 4 18 3 36 Plant 3 19 2 38 Plant 2 20 1 39 FAUCET 22 0 39 Plant 1 23 3 42 FAUCET 24 2 44 Plan Far: Total steps = 24, total step-units = 44 *** With 7 plants, Plan Far is better with 12 fewer step-units.