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Bebras 2019 - Level 3 Question 14

BEBRAS · Bebras 2019 - Level 3

Question 14

Tara the beaver wants to go home. At each step she can move one square up or one square right in the diagram below.

Question illustration

Each square contains coins or starfish. Whenever she crosses a square containing coins, she takes all its coins. Whenever she crosses a square with starfish, she must leave as many coins as there are starfish. If she has no coins left, she can pay later when she has more. What is the largest number of coins Tara can have when she gets home?

Editable grid data: positive values are coins collected, negative values are starfish payments; the lower-left 0 is the start and upper-right 0 is home.

| Row from top | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1 | 1 | -2 | 3 | 3 | 0 |
| 2 | -2 | 1 | -2 | -1 | 2 |
| 3 | 2 | -2 | 2 | 3 | -1 |
| 4 | 3 | -1 | -1 | -1 | 1 |
| 5 | 0 | 2 | 2 | -2 | 2 |
  1. 8
  2. 9
  3. 10
  4. 12