1052 toothpicks can be grouped into 4 groups of third power of 6 (
), 5 groups of second power of 6 (
), 1 group of first power of 6 (
) and 2 groups of zeroth power of 6 (
).
The number 1052, written as a base 6 number is 4512
Given: 1052 toothpicks
To do: The objective is to group the toothpicks in powers of 6 and to write the number 1052 as a base 6 number
First we note that, 
This implies that 
exceeds 1052 and thus the highest power of 6 that the toothpicks can be grouped into is 3.
Now, 
and 
. This implies that 
exceeds 1052 and thus there can be at most 4 groups of .
Then,
So, after grouping the toothpicks into 4 groups of third power of 6, there are 188 toothpicks remaining.
Now, 
and 
. This implies that 
exceeds 188 and thus there can be at most 5 groups of .
Then,
So, after grouping the remaining toothpicks into 5 groups of second power of 6, there are 8 toothpicks remaining.
Now, 
and 
. This implies that 
exceeds 8 and thus there can be at most 1 group of .
Then,
So, after grouping the remaining toothpicks into 1 group of first power of 6, there are 2 toothpicks remaining.
Now, 
and 
. This implies that the remaining toothpicks can be exactly grouped into 2 groups of zeroth power of 6.
This concludes the grouping.
Thus, it was obtained that 1052 toothpicks can be grouped into 4 groups of third power of 6 (), 5 groups of second power of 6 (), 1 group of first power of 6 () and 2 groups of zeroth power of 6 ().
Then,
So, the number 1052, written as a base 6 number is 4512.
Learn more about change of base of numbers here:
brainly.com/question/14291917
