What Is the Missing Digit in \(1995^{10}\)?

  • MHB
  • Thread starter anemone
  • Start date
In summary, the "Find the Missing Digit" problem involves a given number, $1995^{10}$, with one digit missing. It is a challenging problem that can be solved using algebraic equations and manipulation or by testing different combinations of digits. There are also patterns and tricks that can aid in solving the problem. This problem is important in mathematics as it helps develop critical thinking and problem-solving skills, reinforces concepts, and emphasizes the importance of precision and accuracy in calculations.
  • #1
anemone
Gold Member
MHB
POTW Director
3,883
115
Here is this week's POTW:

-----

Find the digit $X$ such that $9986860883748524X5070273447265625$ equals $1995^{10}$.

-----

Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!
 
Physics news on Phys.org
  • #2
Congratulations to the following members for their correct solution!(Cool)

1. kaliprasad
2. castor28
3. Olinguito
4. greg1313
5. lfdahl

Solution from kaliprasad:
Because 1995 is divisible by 3 so all the powers $\ge 2$ of 1995 shall be divisible by 9.
So sum of digits of the result must be divisible by 9.
We get sum of digits of given number = 160 + X.
Smallest multiple of 9 above 160 is 162 which gives X= 2 and next multiple of 9 gives x = 11. So X= 2 is the right answer.
 

FAQ: What Is the Missing Digit in \(1995^{10}\)?

What is the "Find the Missing Digit" problem?

The "Find the Missing Digit" problem involves a given number, in this case $1995^{10}$, where one digit is missing. The goal is to determine what the missing digit is based on the given information.

What is the significance of the number $1995^{10}$ in this problem?

The number $1995^{10}$ is significant because it is a large number with a missing digit, making it a challenging problem to solve.

How can I solve the "Find the Missing Digit" problem?

One approach to solving this problem is by using algebraic equations and manipulation to narrow down the possible values for the missing digit. Another approach is by using a calculator or computer program to test different combinations of digits until the correct one is found.

Are there any patterns or tricks that can help solve this problem?

Yes, there are several patterns and tricks that can be used to help solve the "Find the Missing Digit" problem. For example, looking for patterns in the given number or breaking it down into smaller parts can make the problem easier to solve.

Why is this problem important in the field of mathematics?

This problem is important in the field of mathematics because it helps develop critical thinking and problem-solving skills. It also reinforces concepts such as algebraic equations, patterns, and numerical operations. Additionally, it can be used to demonstrate the importance of precision and accuracy in mathematical calculations.

Similar threads

MHB What Is the Sum of the Digits of 3n Given These Conditions?
Replies
1
Views
1K
MHB What Is the Missing Digit in $2^{29}$?
Replies
1
Views
1K
MHB POTW #374: Finding the 1000th Digit of the Square Root of a Large Number
Replies
1
Views
1K
MHB Find the Smallest Divisible Integer: POTW #405 Feb 20th, 2020
Replies
1
Views
1K
MHB Perfect Squares as Divisors of $1!\cdot 2! \cdot 3! \cdots 9!$
Replies
1
Views
1K
MHB Is ln(2) Greater Than (2/5)^(2/5)?
Replies
2
Views
2K
MHB How Can You Factorize the Polynomial (x+1)(x+2)(x+3)(x+6)-3x^2?
Replies
1
Views
1K
MHB Can You Solve This Trigonometric Inequality?
Replies
1
Views
1K
MHB Can You Solve This Cubic and Square Root Equation?
Replies
1
Views
1K
MHB What is the solution for d in a trigonometric equation with multiple terms?
Replies
1
Views
1K

Recent Insights

Back
Top