Solve This!
Palindromes
What is a Palindrome?
What is a palindrome? A palindrome is a word or a sentence or number that is the same turned around, like kayak. If you read it backwards, it’s the same word. We used numbers; not words.
Word Palindromes
- radar
- mom
- dad
Sentence Palindrome
Number Palindromes
- 76067
- 416614
- 59695
- 374473
- 87966978
- 987654321123456789
What were we investigating?
We were trying to figure out how many steps it takes to get to a palindrome from the number we started with. We tested the numbers 10 through 100. If we started with 13, we would then turn 13 around to get 31, then we added them together to get 44, and 44 is a palindrome. We called this a one step palindrome.
But if you have a number like 68, then you add 68 and 86 [because 86 is the reverse of 68], and you get 154. Then you have to do the reverse of 154 to get 451, then you add together 154 and 451 to get 605. Then you do the reverse of 605 to get 506, then you add 605 and 506 to get 1111, which is a palindrome. We called this a three step palindrome.
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13
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68
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+31
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+86
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44
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154
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+ 451
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605
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+506
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1111
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How did we organize the results?
We found out how many steps each number took, and we color coded the numbers. After we figured out how many steps each number took we color coded: 0 steps blue, 1 step orange, 2 steps green, 3 steps yellow, 4 steps pink, 6 steps red and 24 steps purple.
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10
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11
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12
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13
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14
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15
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16
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17
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18
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19
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20
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21
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22
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23
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24
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25
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26
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27
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28
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29
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30
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31
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32
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33
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34
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35
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36
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37
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38
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39
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40
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41
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42
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43
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44
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45
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46
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47
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48
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49
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50
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51
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52
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53
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54
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55
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56
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57
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58
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59 |
60
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61
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62
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63
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64
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65
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66
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67
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68
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69
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70
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71
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72
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73
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74
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75
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76
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77
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78
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79
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80
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81
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82
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83
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84
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85
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86
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87
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88
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89
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90
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91
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92
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93
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94
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95
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96
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97
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98
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99 |
100
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What did we discover?
We discovered that:
If you do one number like 26, when you find out it is a one step number, then 62 is a one step number, because it’s just 26 turned around to 62.
Most of the numbers are one step numbers between 1 and 100.
There are some numbers that are 0 steps like 11 because it is a palindrome already.
The biggest number of steps is 24 and there are only two 24 step numbers and they are 98 and 89.
There are 0 steps, 1 step, 2 steps, 3 steps, 4 steps, 6 steps, 24 steps.
There were 17 final palindromes:
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11
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22
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33
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44
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55
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66
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77
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88
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99
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101
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121
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363
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484
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1111
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4884
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44,044
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8,813,200,023,188
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All the palindromes are divisible by 11 except for 101 which was the final palindrome for 100!!!!!
Click here to help us find palindromes for numbers higher than 100.