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MathMagic Cycle 16: Level 4-6 Regular

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                                             9   10   11   13   21
Magic Rows                                 ---- ---- ---- ---- ----
                                          |    |    |    |    |    |
1- Using the grid on the right pick     0 |  9 | 10 | 11 | 13 | 21 |
   any number from the chart. Draw a      |    |    |    |    |    |
   a circle around it and cross out        ---- ---- ---- ---- ----
   all the other numbers on the same      |    |    |    |    |    |
   row and the same column.             1 | 10 | 11 | 12 | 14 | 22 |
                                          |    |    |    |    |    |
2- Pick another number that has not        ---- ---- ---- ---- ----
   been crossed out, circle it and        |    |    |    |    |    |
   cross out the row/column numbers.    2 | 11 | 12 | 13 | 15 | 23 |
   Repeat this process until you have     |    |    |    |    |    |
   five circled numbers. They should       ---- ---- ---- ---- ----
   all be in different rows and           |    |    |    |    |    |
   columns.                             3 | 12 | 13 | 14 | 16 | 24 |
                                          |    |    |    |    |    |
3- Add the circled numbers. Your answer    ---- ---- ---- ---- ----
                                          |    |    |    |    |    |
   is: ___________                      15| 24 | 25 | 26 | 28 | 36 |
                                          |    |    |    |    |    |
4- Copy the figure on another paper 3      ---- ---- ---- ---- ----
   times and choose different numbers.
   Add them up. What are the answers?   _________ , __________, __________

5- Try to explain the answer - why is it happening? Does it work with any
   set of numbers?

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MathMagic Cycle 16: Level 4-6 Advanced

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Palindromes (Quick, look it up in the math dictionary) Definition:

One of the most famous palindromes was about a US president:
          A man, a plan, a canal - Panama!             Who:

A number such as 1331 is also a palindrome. It has "bilateral symmetry".
If "bi" means two, what do you think that concept means? Does 1356531
have bilateral symmetry? Explain.

A famous unsolved number problem called the "palindrome conjecture" says
that you can start with any number greater than 10, reverse it, and add
the two numbers. After a certain number of times repeating this process,
you will come up with a palindrome:

1) 86+68=154  2) 154+451= 605  3) 605+506= 1111 which is a palindrome.

Experiment with say five numbers. Try to stay in the range of 10 to 1000.
How many steps did you have to do before a palindrome came up?

Try 196. What appears to happen?

By using a few examples, can you show that the statement "Every palin-
dromic number with an even number of digits is a multiple of 11" is in
fact a true statement?

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