How many carrots can the trader sell in total?
A businessman rides a donkey across a 1000 km long desert and the businessman has 3000 carrots. The donkey can carry 1000 carrots at a time and eats one carrot per kilometer.
How many carrots can the trader sell in total?
The answer is 534.
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1 solution
How does it happen??
The donkey cannot carry the carrots from A to B nonstop or everything will be turned into fueling the donkey, so we need to appoint R&Rs along the journey to enable them to unload some of the 'surviving' carrots before making more trips back and fro until that stage of the distance is cleared. We use the sacrificial carrots in lots of 1000 to match the maximum capacity of that donkey. In the first stage, the minimum forward trip they have to make is 3000 / 1000 = 3, but the donkey would need feeding on the return trips, too, so we multiply by the forward trips by 2, save the last one since everything is already moved to the next pitstop (that's the -1 there).
What we calculated in the round brackets is the rest of the distance after the 2 pitstops reached (distance calculations shown in two pairs of square brackets), and we reduce that from the last carriage of 1000 carrots as donkey's food.
1000 km distance
= (City A) + 200 + (RnR1) + 333⅓ + (RnR2) + 466⅔ + (City B)
Legend
?? : Action done on the carrots
L : Loading
UL : Unloading
IT : In-Transit
→ : Forward direction
← : Backward direction
{} : Total carrots consumed between the same 2 stops
| A | 1st leg | RnR1 | 2nd leg | RnR2 | 3rd leg | B | ?? |
| 3000 | L | ||||||
| 2000 | 1000 | IT→ | |||||
| 2000 | {200} | 800 | UL | ||||
| 2000 | 200 {200} | 600 | ←IT | ||||
| 2000 | {400} | 600 | L | ||||
| 1000 | 1000 {400} | 600 | IT→ | ||||
| 1000 | {600} | 1400 | UL | ||||
| 1000 | 200 {600} | 1200 | ←IT | ||||
| 1000 | {800} | 1200 | L | ||||
| 0 | 1000 {800} | 1200 | IT→ | ||||
| 0 | {1000} | 2000 | L | ||||
| 0 | {1000} | 1000 | 1000 | IT→ | |||
| 0 | {1000} | 1000 | {333⅓} | 666⅔ | UL | ||
| 0 | {1000} | 1000 | 333⅓ {333⅓} | 333⅓ | ←IT | ||
| 0 | {1000} | 1000 | {666⅔} | 333⅓ | L | ||
| 0 | {1000} | 0 | 1000 {666⅔} | 333⅓ | IT→ | ||
| 0 | {1000} | 0 | {1000} | 1000 | L | ||
| 0 | {1000} | 0 | {1000} | 0 | 1000 | IT→ | |
| 0 | {1000} | 0 | {1000} | 0 | {466⅔} | 533⅓ | UL |
A n s w e r
= 1 0 0 0 − ( 1 0 0 0 − [ 1 0 0 0 / ( 3 × 2 − 1 ) ] − [ 1 0 0 0 / ( 2 × 2 − 1 ) ] )
= 1 0 0 0 − ( 1 0 0 0 − [ 2 0 0 ] − [ 3 3 3 ⅓ ] )
= 5 3 3 ⅓
1000 km distance
= (City A) + 200 + (RnR1) + 333⅓ + (RnR2) + 466⅔ + (City B)