How many tens are in a thousand?

Answer 1

• The answer to: How many tens are in a thousand?
  

There are one hundred, tens in a thousand. 100 * 10 = 1000.

• The generic solution would be:

If you have a number X and you want to see how many of the numbers between 0 and X are divisible by a number Y... Simply divide X/Y. In the example above, 1000 / 10 = 100.

• Both an exhaustive reasoning and a recursive solution:
  

1. How many tens are there in 10?
2. 1. Well, we must search the problem space of the the numbers between [0...10]. Non math folks, this just means every number from 0 to 10 which would be [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].
   2. As you can plainly see, 10 is a member of this list but no other number is evenly divisible by 10. In fact, no other number besides the '10' from the list is greater than our desired value 10. Therefore, there can only be 1 ten in 10.

1. How many tens are in 100?
2. 1. Now we search the problem space of [0...100]. We notice this includes several values greater than 10 so we should begin to suspect that there are several multiples of 10 in the list. If we exhaustively compare each of the numbers in the list to 10, we realize that 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 are all multiples of 10... We have found 10 matches so there must be ten 10's in 100.
   2. Recursively, we could have done this by realizing that... There is ONE 10 in the value 10 and the number 100 contains TEN instances of the value 10. Therefore: 10 (number of TENS in 100) * 1 (number of TENS in 10) = 10.

1. How many tens are in 1000?
2. 1. We could exhaustively search the problem space from [0...1000] and find out there are 100 values that are divisible by ten, but that would be silly. We can use information from our previous calculations to develop some neat rules and relationships.
   2. We know that there's ONE 10 in the number 10
   3. We know that there's TEN 10's in the number 100.
   4. We also already know (from step 2.1 and 2.2) that 100 is composed of TEN 10's. We also know that the number 1000 is composed of TEN 100's. These values would be: 100, 200, 300, 400, 500, 600, 700, 800, 900, 100. So, in total we have that 1000 is composed of TEN 100's and each 100 is composed of TEN 10's. In order to determine the total number of 10's in 1000 intelligently, we must multiply 10 (the total number of 100's in 1000) * 10 (the number of 10's in each 100) * 1 (the total number of 10's in each 10) = 100.
      

Answer 2

7

000000

Answer 3

100

Answer 4

10

Answer 5

2

Answer 6

10

Answer 7

100