Problem 5 beginning at part 3 please. Part 5 is unnecessary.

p C Power Sets Of Empty Sets: What x G how to screenshot - Google Sear x + - 0 X + cs 1800 (3 unread) X N cs1800sp20_hw3.pdf X C Get Homework Help With Chegg * c Not secure ccs.neu.edu/home/rachlin/discrete/hw/cs 1800sp20_hw3.pdf Apps Yahoo B Blackboard N myNEU T TopHat Canvas Il Gradescope N Discrete Other bookmarks cs 1800sp20_hw3.pdf 3/3 Problem 5 (20 pts): Thought Problems i. For how many numbers from 5000 to 7999 do the digits add up to an odd number? Hint. Use a one-to-one map, follow these steps: 1. define the set A of numbers with desired property in given range, and the set , with the others 2. describe a one-to-one map (pairing) that associates every element in A with a unique element in A and viceversa 3. conclude that the two sets have the same size, and calculate the size of A ii. P(P(P(0 x 0))) =? iii. A piece of math paper has been wrapped onto a cylinder to create the figure below. It has 12 rows and 35 columns. Three cells of the grid are marked A,B,X. An ant can start on bottom row in location A or location B, then work a path up to the top row by stepping one row at a time either straight-up, or diagonal-left, or diagonal-right. Explain why any such path must have exactly 11 moves. How many different possible paths can an ant take, starting at position A or B? iv. The same question as before (count the paths). Ants can start on any square in the bottom row but now cannot pass through cell X. Hint: Count the paths passing through X as a combination of two paths: X start (reversed) and X finish. v. (optional, no credit, *) The same question as before but now ants must start on A or B, and are not allowed to pass through cell X. p C Power Sets Of Empty Sets: What x G how to screenshot - Google Sear x + - 0 X + cs 1800 (3 unread) X N cs1800sp20_hw3.pdf X C Get Homework Help With Chegg * c Not secure ccs.neu.edu/home/rachlin/discrete/hw/cs 1800sp20_hw3.pdf Apps Yahoo B Blackboard N myNEU T TopHat Canvas Il Gradescope N Discrete Other bookmarks cs 1800sp20_hw3.pdf 3/3 Problem 5 (20 pts): Thought Problems i. For how many numbers from 5000 to 7999 do the digits add up to an odd number? Hint. Use a one-to-one map, follow these steps: 1. define the set A of numbers with desired property in given range, and the set , with the others 2. describe a one-to-one map (pairing) that associates every element in A with a unique element in A and viceversa 3. conclude that the two sets have the same size, and calculate the size of A ii. P(P(P(0 x 0))) =? iii. A piece of math paper has been wrapped onto a cylinder to create the figure below. It has 12 rows and 35 columns. Three cells of the grid are marked A,B,X. An ant can start on bottom row in location A or location B, then work a path up to the top row by stepping one row at a time either straight-up, or diagonal-left, or diagonal-right. Explain why any such path must have exactly 11 moves. How many different possible paths can an ant take, starting at position A or B? iv. The same question as before (count the paths). Ants can start on any square in the bottom row but now cannot pass through cell X. Hint: Count the paths passing through X as a combination of two paths: X start (reversed) and X finish. v. (optional, no credit, *) The same question as before but now ants must start on A or B, and are not allowed to pass through cell X