PIKO · LEARN & EXPLAIN
Water jugs: calculate the space left
Track two quantities at once and calculate how much can move between containers without markings.
Before you start
You need subtraction with small whole numbers. Treat this as a paper puzzle; no water equipment is required.
Work through this example
Jug A holds 3 L and B holds 5 L. Both start empty. You may fill a jug, empty it or pour into the other until the source is empty or the receiver is full. Leave 4 L in B within six operations.
| Operation | A (L) | B (L) |
|---|---|---|
| Start | 0 | 0 |
| 1. Fill B | 0 | 5 |
| 2. Pour B into A | 3 | 2 |
| 3. Empty A | 0 | 2 |
| 4. Pour B into A | 2 | 0 |
| 5. Fill B | 2 | 5 |
| 6. Pour B into A | 3 | 4 |
Reason step by step
- Fill B, then pour B into A. A can take 3 L, leaving the state (A,B) = (3,2).
- Empty A, then move B’s remaining 2 L into A. Now (A,B) = (2,0). Filling B again gives (2,5).
- A has room for only 3 − 2 = 1 L. Pouring from B transfers 1 L, leaving (3,4). The target is reached after six operations.
A mistake worth understanding
Do not subtract A’s full capacity every time. In the last pour A is not empty. The amount transferred is min(source water, free receiving space).
Try it yourself
Restart with empty jugs. How can you leave exactly 2 L in B using two operations? Why can you not simply stop pouring B after 1 L without using A?
Show the answer and reasoning
Fill B and pour into empty A: (0,5) → (3,2). Without markings, an arbitrary 1 L stopping point is not an allowed operation.
Use the idea in the game
In the game, read both capacities and the target again. Reaching the target in either jug counts; the six-step sequence here applies to this example, not every generated puzzle.
Open the activity →About & help
These examples were written for Piko Game. Generated game questions may differ. A score describes a game attempt, not mastery of a school curriculum.
Found an error? Send the page address and the step that needs checking to j565718319@gmail.com。
What each learning map contains