Solve the following pattern problems.

G. Solve the following problems. 1. Magic Square. A magic square is an arrangement of numbers in a square such that all rows. all columns. and both main diagonals sum to the same number. a number referred to as the magic constant. The square on the right is perhaps the best-known example of a magic square. Complete the magic square below so that the sum of the verticals. horizontals and diagonals is Is. 2. Tower of Hanoi. The Tower of Hanoi "is a logical puzzle. frequently studied in cognitive psychology and used as a test of problem-solving ability. consisting of three pegs. on one of which are placed a number of discs of varying diameter, the largest at the bottom and the smallest at the top. H H H H The problem is to move the tower of discs over to one of the other pegs in the smallest number of moves. moving one disc at a time and using the third peg as a temporary way station as required. and never placing a larger disc on top of a smaller one. How many moves are necessary to place all 6 discs to the third peg? 8 A book has 89 pages but the page numbers are printed incorrectly. Every third page number has been omitted, so that the pages are numbered 1.1.4.5 7. 8... .and so on. What is the number on the last primed page? 9. Lola's watch gains 30 minutes every hour. while Lolo's watch loses 30 minutes every hour. At midnight. they both set their watches to the correct time of 12 o'clock. What is the correct time when their tum watches next agree?? . 10. Kenneth sent 29 e- -mails on Wednesday. 3? e-mails on Thursday. 45 e-mails on Friday. 53 e-mails on Saturday. and 6] e- mails on Sunday If this pattern continues. how many e-mails will Kenneth send on Monday? 11. Ruben decides to prepare for a marathon by running ten minutes a day. six days a week. Each week. he increases his time running by two minutes per day. How many minutes will he run in week 8? 12. Angela is making a box without a lid. She starts with a 20 in. square piece of cardboard and cuts out ' - ,four equal squares from each corner of the cardboard as shown. She then folds the sides of the box and glues the edges together. How big does she need to cut the corner squares in order to make the box with the biggest volume