************************************* MathMagic Cycle 16: Level 4-6 Regular ************************************* 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? ************************************** MathMagic Cycle 16: Level 4-6 Advanced ************************************** 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? ==================