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A palindrome is an integer that reads the same forwards and backward. How many positive 3-digit palindromes are multiples of 3?

Dec 14, 2018

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+23137
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A palindrome is an integer that reads the same forwards and backward.

How many positive 3-digit palindromes are multiples of 3?

$$\begin{array}{|r|r|r|r|} \hline & n & \text{palindrome } a(n) & \text{divisible by } 3 \\ \hline & 20& 1 01 \\ 1. & 21& 1 11 & \checkmark \\ & 22& 1 21 \\ & 23& 1 31 \\ 2. & 24& 1 41 &\checkmark \\ & 25& 1 51 \\ & 26& 1 61 \\ 3.& 27& 1 71 &\checkmark \\ & 28& 1 81 \\ & 29& 1 91 \\ \hline & 30& 2 02 \\ & 31& 2 12 \\ 4. & 32& 2 22 &\checkmark \\ & 33& 2 32 \\ & 34& 2 42 \\ 5. & 35& 2 52 &\checkmark \\ & 36& 2 62 \\ & 37& 2 72 \\ 6.& 38& 2 82 &\checkmark \\ & 39& 2 92 \\ \hline 7. & 40& 3 03 &\checkmark \\ & 41& 3 13 \\ & 42& 3 23 \\ 8. & 43& 3 33 &\checkmark \\ & 44& 3 43 \\ & 45& 3 53 \\ 9. & 46& 3 63 &\checkmark \\ & 47 & 3 73 \\ & 48& 3 83 \\ 10. & 49& 3 93 &\checkmark \\ \hline & 50& 4 04 \\ 11. & 51& 4 14 &\checkmark \\ & 52& 4 24 \\ & 53& 4 34 \\ 12. & 54& 4 44 &\checkmark \\ & 55& 4 54 \\ & 56& 4 64 \\ 13. & 57& 4 74 &\checkmark \\ & 58& 4 84 \\ & 59& 4 94 \\ \hline & 60& 5 05 \\ & 61& 5 15 \\ 14. & 62& 5 25 &\checkmark \\ & 63& 5 35 \\ & 64& 5 45 \\ 15. & 65& 5 55 &\checkmark \\ & 66& 5 65 \\ & 67& 5 75 \\ 16. & 68& 5 85 &\checkmark\\ & 69& 5 95 \\ \hline 17. & 70& 6 06 &\checkmark \\ & 71& 6 16 \\ & 72& 6 26 \\ 18. & 73& 6 36 &\checkmark \\ & 74& 6 46 \\ & 75& 6 56 \\ 19. & 76& 6 66 &\checkmark \\ & 77& 6 76 \\ & 78& 6 86 \\ 20. & 79& 6 96 &\checkmark \\ \hline & 80& 7 07 \\ 21. & 81& 7 17 &\checkmark \\ & 82& 7 27 \\ & 83& 7 37 \\ 22. & 84& 7 47 &\checkmark \\ & 85& 7 57 \\ & 86& 7 67 \\ 23. & 87& 7 77 &\checkmark \\ & 88& 7 87 \\ & 89& 7 97 \\ \hline & 90& 8 08 \\ & 91& 8 18 \\ 24. & 92& 8 28 &\checkmark \\ & 93& 8 38 \\ & 94& 8 48 \\ 25. & 95& 8 58 &\checkmark \\ & 96& 8 68 \\ & 97& 8 78 \\ 26. & 98& 8 88 &\checkmark \\ & 99& 8 98 \\ \hline 27. & 100& 9 09 &\checkmark \\ & 101& 9 19 \\ & 102& 9 29 \\ 28. & 103& 9 39 &\checkmark \\ & 104& 9 49 \\ & 105& 9 59 \\ 29. & 106& 9 69 &\checkmark \\ & 107& 9 79 \\ & 108& 9 89 \\ 30. & 109& 9 99 &\checkmark \\ \hline \end{array}$$

30  3-digit palindromes are divisible by 3.

Dec 14, 2018

#1
+23137
+10

A palindrome is an integer that reads the same forwards and backward.

How many positive 3-digit palindromes are multiples of 3?

$$\begin{array}{|r|r|r|r|} \hline & n & \text{palindrome } a(n) & \text{divisible by } 3 \\ \hline & 20& 1 01 \\ 1. & 21& 1 11 & \checkmark \\ & 22& 1 21 \\ & 23& 1 31 \\ 2. & 24& 1 41 &\checkmark \\ & 25& 1 51 \\ & 26& 1 61 \\ 3.& 27& 1 71 &\checkmark \\ & 28& 1 81 \\ & 29& 1 91 \\ \hline & 30& 2 02 \\ & 31& 2 12 \\ 4. & 32& 2 22 &\checkmark \\ & 33& 2 32 \\ & 34& 2 42 \\ 5. & 35& 2 52 &\checkmark \\ & 36& 2 62 \\ & 37& 2 72 \\ 6.& 38& 2 82 &\checkmark \\ & 39& 2 92 \\ \hline 7. & 40& 3 03 &\checkmark \\ & 41& 3 13 \\ & 42& 3 23 \\ 8. & 43& 3 33 &\checkmark \\ & 44& 3 43 \\ & 45& 3 53 \\ 9. & 46& 3 63 &\checkmark \\ & 47 & 3 73 \\ & 48& 3 83 \\ 10. & 49& 3 93 &\checkmark \\ \hline & 50& 4 04 \\ 11. & 51& 4 14 &\checkmark \\ & 52& 4 24 \\ & 53& 4 34 \\ 12. & 54& 4 44 &\checkmark \\ & 55& 4 54 \\ & 56& 4 64 \\ 13. & 57& 4 74 &\checkmark \\ & 58& 4 84 \\ & 59& 4 94 \\ \hline & 60& 5 05 \\ & 61& 5 15 \\ 14. & 62& 5 25 &\checkmark \\ & 63& 5 35 \\ & 64& 5 45 \\ 15. & 65& 5 55 &\checkmark \\ & 66& 5 65 \\ & 67& 5 75 \\ 16. & 68& 5 85 &\checkmark\\ & 69& 5 95 \\ \hline 17. & 70& 6 06 &\checkmark \\ & 71& 6 16 \\ & 72& 6 26 \\ 18. & 73& 6 36 &\checkmark \\ & 74& 6 46 \\ & 75& 6 56 \\ 19. & 76& 6 66 &\checkmark \\ & 77& 6 76 \\ & 78& 6 86 \\ 20. & 79& 6 96 &\checkmark \\ \hline & 80& 7 07 \\ 21. & 81& 7 17 &\checkmark \\ & 82& 7 27 \\ & 83& 7 37 \\ 22. & 84& 7 47 &\checkmark \\ & 85& 7 57 \\ & 86& 7 67 \\ 23. & 87& 7 77 &\checkmark \\ & 88& 7 87 \\ & 89& 7 97 \\ \hline & 90& 8 08 \\ & 91& 8 18 \\ 24. & 92& 8 28 &\checkmark \\ & 93& 8 38 \\ & 94& 8 48 \\ 25. & 95& 8 58 &\checkmark \\ & 96& 8 68 \\ & 97& 8 78 \\ 26. & 98& 8 88 &\checkmark \\ & 99& 8 98 \\ \hline 27. & 100& 9 09 &\checkmark \\ & 101& 9 19 \\ & 102& 9 29 \\ 28. & 103& 9 39 &\checkmark \\ & 104& 9 49 \\ & 105& 9 59 \\ 29. & 106& 9 69 &\checkmark \\ & 107& 9 79 \\ & 108& 9 89 \\ 30. & 109& 9 99 &\checkmark \\ \hline \end{array}$$

30  3-digit palindromes are divisible by 3.

heureka Dec 14, 2018