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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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