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A palindrome is a number that reads the same forward and backward. For
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Updated on: 24 Jul 2019, 10:04
Take the palindrome as ABCACBA A = 5 or 6 >> 2 possibilities B = 5 or 6 or 0 >> 3 possibilities C = 5 or 6 or 0 >> 3 possibilities Middle single A = 5 or 6 or 0 >> 3 possibilities So total numbers = 2*3*3*3 = 54 Corrected the mistake and reposted
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Originally posted by Jiggy11 on 22 Jul 2019, 12:05.
Last edited by Jiggy11 on 24 Jul 2019, 10:04, edited 1 time in total.



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 12:16
A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?
A. 16 B. 54 C. 81 D. 486 E. 729
To form a 7 digit number, the first digit can't be 0, so only 2 ways to choose the 1st digit  5 or 6. 2nd digit could be one of 5, 6, 0  hence 3 ways to choose 3rd digit also could be one of 5,6,0  hence 3 ways to choose 4th digit also could be one of 5, 6, 0  hence 3 ways to choose.
The remaining digits are all a mirror of the 1st three, hence only 1 way to choose.
So, final answer = 2*3*3*3*1*1*1 = 54.
Correct answer B



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 12:36
A sevendigit palindrome: \(ABSDSBA\) We can use any of or all of the following digits: \(5, 6, 0\) Examples of palindrom: \(5555555, 6665666, 5006005,\) but not \(0560650\). The last one is a sixdigit number, so we can't use \(0\) as the starting digit. Correspondingly, we have \(2\) choices (\(5\) and \(6\)) for \(A\), and by \(3\) choices (\(5,6,\) and \(0\)) for each of \(B, S,\) and \(D\). The number of possible palindromes: \(2*3*3*3=54\) Hence B
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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 12:47
A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?
Let's say that _ is missing digit: _ _ _ _ _ _ _  7 digits And there are 3 possible variants of digit: 5,6,0 So the first digit can be 5 and 6 (if 0 it's not 7 digit number) 2*3*3*3*1*1*1 = 54 Why is the last 3 digits 1 ? Because this number is a palindrome, that has the same end as the beginning.
ANSWER B
A. 16 B. 54 C. 81 D. 486 E. 729



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 12:52
IMO Correct answer is B; Explanation is provided as attachment
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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 13:03
7 digit palindrome would be like ABCDCBA. So we have for A: two options: 5 or 6 rest B,C &Dcan be any of the 3 options. therefore answer is 2*3*3*3=54



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 13:28
A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?
A. 16 B. 54 C. 81 D. 486 E. 729
The question looks scary, especially when we see the range of the given answers. But hold on, it is not so hard! First of all, let's imagine the possible 7digit palindromes. It is clear that we are interested only in first 4 digits, because the last 3 digits will copy the first 3. Besides, we know that the first digit can't be zero. So we have 2 possible options (5 and 6) for the first digit and 3 options (5, 6, 0) for each of the remaining 3 digits. 2*3*3*3 = 54
The answer is B



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 15:02
The digits to choose from to create palindromes are 5,6, and 0. Since we are to create 7 figure palindromes, there is a restriction on position 1 from the available digits. 0 cannot be the first digit and by extension, it cannot be the last digit. Therefore, we are limited to the selection of either 5 or 6 and there are 2C1 possible ways of selecting either for the first and seventh digit.
Second, third and fourth digit do not have any restrictions. Therefore there are 3C1 ways of selecting a number among the three digits to fill those positions.
The total number of possible palindromes that can be created is therefore given as: 2C1*3C1*3C1*3C1=2*3*3*3=54. The answer is therefore B.
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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 16:35
Given: there are 3 number choices (5,6,0)
For 7th digit to be palindrome, 17, 26, 35 must be same number. 4th digit can be any number.
so there are 3 choices for pair (17), pair (26), pair (35) and (4)
thus 3*3*3*3 = 3^4 = 81.
Answer is C



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 16:38
Any 7digit palindromes can be written as 'abcdcba'.
Number of values that a can take= 2 (5 or 6)
Number of values that b, c and d can take= 3 (0, 5 or 6)
Total number of 7digit palindromes using 0, 5 and 6 = 2*3*3*3*1*1*1= 54
IMO B



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 17:23
Palindrome of 7 digits > XYZPZYX Digits to choose from  5, 6, 0 how many palindromes are possible ? As we can see we have to find only X, Y, Z, P > combinations in Mix first digit cannot be 0 ; X can be 5 or 6 X = 2 ways (5, 6) Y = 3 ways (5, 6, 0) Z = 3 ways (5, 6, 0) P = 3 ways (5, 6, 0)
total ways = 2 * 3 * 3 * 3 = 54 ways
B is the answer!



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A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 18:15
Let the 7digit number be a b c d c b a.
So, we only need to find out how many we can fill a, b, c and d, because the last three digits take the same number. In addition to that, all a, b, c, and d have to be of the digits 5, 6 and 0 (repetition is allowed) • a can take \(2\) numbers, which are 5 and 6. 0 is definitely out. • b can take \(3\) numbers, which are 0, 5 and 6. • c can take \(3\) numbers, which are 0, 5 and 6. • d can take \(3\) numbers, which are 0, 5 and 6.
Thus, way to form a 7digit palindrome number formed using one or more of the digits 5, 6 and 0 = \(2 * 3 * 3 * 3 * 1 * 1 * 1= 54\).
Answer is option (B) \( 54\)



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 19:13
Answer is 81.
This is because while it is a 7 letter combination, you actually only have 4 slots to fill because the first and last is the same (1st slot), 2nd and 6th (2nd slot), 3rd and 5th (3rd slot) and finally the 4th.
So because you have 3 numbers to choose from with replacement, the choices are 3 x 3 x 3 x 3
Ie 81
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A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 19:17
the number can be constructed from 3 digits 5,6,0. Zero cannot be in first digit place. So only 2 ways of arranging the first digit. the middle point is digit 4. Digit 2 to digit 4 can be arranged in 3 ways each. The remaining digits can only be arranged in one way since this is a palindrome. Total possible ways= 2*3*3*3*1*1*1=54 ways see the picture. Posted from my mobile device
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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 19:35
A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?
Make 7 slots _ _ _ _ _ _ _ There are 2 possibilities of the first slot (the number cannot start with 0 as this would form a 6 digit number) 2 _ _ _ _ _ _ There are 3 possibilities of the second slot 2 3 _ _ _ _ _ Similar to the second lost, there are 3 possibilities of the third slot and of the fourth slot 2 3 3 3 _ _ _ In order for it to be a palindrome, the fifth slot must be the same as the third slot, 1 possibility 2 3 3 3 1 _ _ Similar logic follows for the last two slots (there can only be one possibility for each for it to be a palindrome) 2 3 3 3 1 1 1 Multiply all together 2*3*3*3*1*1*1 = 54
Answer  B



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 19:52
7 digit palindrome mean it should read the same from 4th digit. Number of ways 1st digit can be filled=2 (since we can't use 0) 2nd digit=3 ways 3rd digit=3 ways 4th digit=3 ways All digits after this can be filled only in 1 way Therefore, total possible palindromes= 2*3^3 = 54 Posted from my mobile device
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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 20:01
XABCBAX
 X can have 2 values  A can have 3 values  B can have 3 values  C can have 3 values
=2*( 3^3)= 54
IMO B



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 20:24
A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?
_ _ _ _ _ _ _ For a palindrome 1st and last should be same. similarly 2nd and 2nd last should be same. There is only one choice for last as it has be same as 1st 1st can only be 2 as 0 not allowed ways to fill 1st and last will be 2 _ _ _ _ _ _ 1 2nd and 2nd last will be 2 *3 _ _ _ _ 1* 1 2 *3*3*3*1*1*1 thus answer 54 B



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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 20:29
A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible? A. 16 B. 54 C. 81 D. 486 E. 729 Sol:A 7digit palindrome will be of the form    a    The first three digits is what wee need to decide, as the last three digits have to be repeated to make a palindrome. For the first digit, we have 2 choices (5 or 6). We can't start the number with 0 as the first digit. For the second digits, we have 3 choices (0, 5 or 6). The digits can be repeated. For the third digit, we have 3 choices (0, 5 or 6). The digits can be repeated. For a, we have 3 choices (0, 5 or 6) Hence, total palindromes that can be made = 2 * 3 * 3 * 3 = 54 The answer is (B).
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Re: A palindrome is a number that reads the same forward and backward. For
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22 Jul 2019, 20:34
A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?
7 digit palindrom = A B C D C B A = 2*3*3*3 *1*1*1 A can can 2 values  5,6 =2 B can take 3 values = 5,6,0 =3 C can take 3 values = 5,6,0 = 3 D can take 3 values = 5,6,0 =3 Next C B A will take only 1 way following the first A B C
Total = 2*3*3*3 *1*1*1 = 27*2 = 54  Option B




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