+0  
 
+1
1195
21
avatar+42 

A palindrome is a number which reads the same forward as backward. How many five-digit palindromes can be made from the digits 1, 2, and 9? (Each digit may be used more than once.)

 

Also, my brother nerdowizard4578's account. Yeah. He can't sign in. It says unknown username.

 Mar 30, 2020
 #1
avatar+2095 
0

Let's list the possibilities...

 

92129

91219

29192

21912

12921

19291

99999

11111

22222

11211

22122

99199

99299

22922

11911

 

So a total of 15 possibilities.

 Mar 30, 2020
edited by CalTheGreat  Mar 30, 2020
 #5
avatar+12 
+3

A five-digit palindrome would be of the form ABCBA, where A, B, and C are digits (not necessarily distinct) from 0 to 9 (with A from 1 to 9). We have three possibilities for each of A, B, and C which gives us 3^3 possible 27 palindromes.

 Mar 30, 2020
 #15
avatar+12 
+1

A five-digit palindrome would be of the form ABCBA, where A, B, and C are digits (not necessarily distinct) from 0 to 9 (with A from 1 to 9). We have three possibilities for each of A, B, and C which gives us 3^3 possible 27 palindromes.

 

                                                                                                                                                    -AoPS Staff

 Mar 30, 2020
edited by JackWang778  Mar 30, 2020

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