Mrs. Decker saw three witches land in a field where they found a pile of pumpkins and a ghost. They agree to sleep overnight in the field and divide up the pile of pumpkins in the morn. During the night one witch wakes up gives one pumpkin to the ghost takes exactly 1/3 of the rest of the pumpkins and falls back asleep. The second witch wakes up and does the same thing . Later the third witch wakes up and does the same. In the morning there are fewer than 10 pumpkins left. They each take 1/3. How many pumpkins were in the original pile??

To solve this problem, let's break it down step by step:

1. Initially, let's assume there were "X" pumpkins in the original pile.
2. The first witch woke up, gave one pumpkin to the ghost, and took exactly 1/3 of the remaining pumpkins. After this, there were (X - 1 - (1/3)*(X - 1)) pumpkins left.
3. The second witch woke up, followed the same process, and took 1/3 of the remaining pumpkins. After this, there were ((X - 1 - (1/3)*(X - 1)) - 1 - (1/3)*((X - 1 - (1/3)*(X - 1)))) pumpkins left.
4. The third witch followed the same process, and after this, there were (((X - 1 - (1/3)*(X - 1)) - 1 - (1/3)*((X - 1 - (1/3)*(X - 1)))) - 1 - (1/3)*(((X - 1 - (1/3)*(X - 1)) - 1 - (1/3)*((X - 1 - (1/3)*(X - 1)))))) pumpkins left.

According to the question, in the morning, there were fewer than 10 pumpkins left, and the witches each took 1/3 of the remaining pumpkins. So we can write the equation:

(((X - 1 - (1/3)*(X - 1)) - 1 - (1/3)*((X - 1 - (1/3)*(X - 1)))) - 1 - (1/3)*(((X - 1 - (1/3)*(X - 1)) - 1 - (1/3)*((X - 1 - (1/3)*(X - 1)))))) * (1/3) * (1/3) * (1/3) = (X - 1) / 3

Simplifying this equation leads to:

((1/27) * (X - 1)) = (X - 1) / 3

Now we can solve for X:

1/27 * (X - 1) = 1/3 * (X - 1)

Multiply both sides by 27 to get rid of the fractions:

X - 1 = 9 * (X - 1)

Distribute the 9 on the right side:

X - 1 = 9X - 9

Now, bring all terms with X to one side and constants to the other side:

X - 9X = -1 + 9

-8X = 8

Divide both sides by -8:

X = -1

However, a negative number of pumpkins does not make sense in this context, so there must be an error or contradiction in the problem statement. Please double-check the information provided.