Calvin's River Crossing Attempt
180 points
Calvin is playing a game of Dungeons and Dragons. In order to make it across the river, he needs to throw six 4-sided dice, and have their sum be a multiple of 5. How many different dice throws result in Calvin making it across the river?
Details and assumptions
The dice are considered distinct from each other.
4^6=4096
1/5 of 4096 is around 819 or 820
try it
its wrong
820
thanks
To find the number of different dice throws that result in Calvin making it across the river, we need to determine the possible sums of rolling six 4-sided dice and then count how many of those sums are multiples of 5.
Here's how we can approach this problem:
1. Determine the range of possible outcomes for each die throw:
- A 4-sided die can have outcomes ranging from 1 to 4, inclusive.
2. Calculate the total number of possible outcomes for all dice throws:
- Since we are throwing six 4-sided dice, the total number of possible outcomes is 4^6 (4 raised to the power of 6) as each die has 4 possible outcomes.
3. Enumerate all possible sums of throwing six 4-sided dice:
- Use nested loops to iterate over all possible combinations of dice outcomes and calculate their sums.
- For example, if the outcomes of the six dice throws are {1, 2, 1, 4, 3, 3}, the sum would be 1 + 2 + 1 + 4 + 3 + 3 = 14.
4. Count the number of sums that are multiples of 5:
- Iterate over all the calculated sums and count how many are divisible by 5 without any remainder.
Let's write a Python code snippet to implement this approach:
```python
from itertools import product
# Step 1: Determine the range of possible outcomes
num_dice = 6
sides = 4
# Step 2: Calculate the total number of possible outcomes
total_outcomes = sides**num_dice
# Step 3: Enumerate all the possible sums
possible_sums = []
for dice_outcomes in product(range(1, sides+1), repeat=num_dice):
possible_sums.append(sum(dice_outcomes))
# Step 4: Count the number of sums that are multiples of 5
count = sum(1 for s in possible_sums if s % 5 == 0)
# Print the result
print(count)
```
By running this code, you'll get the output which represents the number of different dice throws that result in Calvin making it across the river.