PROBLEM 1-7-2


You were given a magic pumpkin patch on October 1st. This pumpkin patch is magic because the number of pumpkins doubles every day. So, on October 1st, your magic pumpkin patch had 1 pumpkin. On October 2nd, you had 2 pumpkins. On October 3rd, you had 4 pumpkins. On October 4th, you had 8 pumpkins. And so on. How many pumpkins will you have on Halloween? Express your answer as a numeral and a power of 2.

SOLUTION 1-7-2

 

By investigating the pattern, you will notice that on the first, the answer is 1 or 20, on the second the answer is 2 or 21, on the third the answer is 4 or 22. So, the pattern is that the power is always one less than the date. So, continuing this pattern, on Oct. 31 the answer 1 073 741 824 is equal to 230.
So, on Halloween there will be 1 073 741 824 = 230 pumpkins in the patch.