ON THE NUMERS 10 AND 100, HOW MANY OF THEM ARE PALINDROMES? PLEASE LIST THEM
FIND PALINDROMES THAT ARE:
A MULTIPLE OF 3
A MULTIPLE OF 4
A MULTIPLE OF 9
A MULTIPLE OF 12
A SQUARE NUMBER
A TRIANGULAR NUMBER
I will do one or two.
33 is one palidrome divisble by 3.
What is 99 divisible by?
Is 121 a plaidrome, and is it square?
You need to do your own thinking on this.
Neither 10 or 100 is a palindrome number. You should know that palindrome nubmbers are numbers that read the same forward and backward, such as 121.
A lion Sound
To find out how many palindromes are there between 10 and 100, you can simply list them out and check if they are palindromic or not:
11, 22, 33, 44, 55, 66, 77, 88, 99
So there are a total of 9 palindromes between 10 and 100.
Now let's find the palindromes that are multiples of certain numbers:
A multiple of 3: Start from the first palindrome, which is 11, and keep adding 11 to find the subsequent palindromes that are multiples of 3. The palindromes that are multiples of 3 are 33 and 99.
A multiple of 4: Palindromes can't be multiples of 4 because all even-digit palindromes are divisible by 11.
A multiple of 9: Start from the first palindrome, which is 11, and keep adding 11 to find the subsequent palindromes that are multiples of 9. The palindrome that is a multiple of 9 is 99.
A multiple of 12: Palindromes can't be multiples of 12 because all even-digit palindromes are divisible by 11.
A square number: Check if the palindrome numbers are squares by finding their square roots. The palindrome 11 has a square root of approximately 3.3166 (not a whole number), so it is not a square number. The palindrome 22 has a square root of approximately 4.6943 (not a whole number), so it is not a square number. Continuing this process, none of the palindromes between 10 and 100 are perfect squares.
A triangular number: Check if the palindrome numbers are triangular numbers by solving the equation (n*(n+1))/2 = palindrome. None of the palindromes between 10 and 100 satisfy this equation and thus are not triangular numbers.
So to summarize:
- The palindromes between 10 and 100 are: 11, 22, 33, 44, 55, 66, 77, 88, and 99.
- The palindromes that are multiples of 3 are: 33 and 99.
- None of the palindromes between 10 and 100 are multiples of 4 or 12.
- The palindrome that is a multiple of 9 is: 99.
- None of the palindromes between 10 and 100 are perfect squares.
- None of the palindromes between 10 and 100 are triangular numbers.
Please note that while I provided explanations for finding the answers, it is always good to attempt these problems yourself to practice and solidify your understanding.