I The How,When,and Why of Mathematics 9 Find a word(written in standard capital letters)that is unchanged when reflected in a horizontal line and in a vertical line.The word must appear in a dictionary(in a language of your choice)in order to be a valid solution. 1."Understanding the problem."We need to find a word.We are given information about the letters that make up this word.There are two conditions:Two different reflections should not alter the word. Try these two reflections on a word,say on SOLUTION,to make sure you un- derstand the problem. 2."Devising a plan."We have to find the connection between what we are given and what we have to find. Which letters of the alphabet satisfy each of the two conditions? Both conditions? Find a word that is not changed if it is reflected in a horizontal line. Find a word that is not changed if it is reflected in a vertical line. Formulate the exact conditions for this exercise;that is,state the letters that can be used and how they must be arranged. 3."Carrying out the plan."Find a word that satisfies the conditions given above. 4.“Looking back.”Are there other solutions? Problem 1.2.Find a word (written in standard capital letters)that reads the same forward and backward and is still the same forward and backward when rotated around its center 180.Your solution needs to appear in a standard dictionary of some language. Problem 1.3.Solve the following anagrams.The first three are places (in the ge- ographical sense),and the fourth is a place in which you might live.All can be rearranged to form a single word. (a)NOVA CURVE: (b)NINE SLAP NAVY: (c)I HELD A HIP PAL: (d)DIRTY ROOM. Note:You may have to find out exactly what an anagram is.This is part of Polya's first point on the list. Problem 1.4.Suppose n teams play in a single game elimination tournament.How many games are played? An example of such tournaments are the various categories of the U.S.Open tennis tournament;for example,women's singles. Note:Pay special attention to the first entry of Polya's list:"Is it possible to satisfy the condition?" Problem 1.5.Suppose you are all alone in a strange house.There are seven identical closed doors.The bathroom is behind exactly one of them.Is it more likely,less likely,or equally likely that you find the bathroom on the first try than on the third try?Why?1 The How, When, and Why of Mathematics 9 Find a word (written in standard capital letters) that is unchanged when reflected in a horizontal line and in a vertical line. The word must appear in a dictionary (in a language of your choice) in order to be a valid solution. 1. “Understanding the problem.” We need to find a word. We are given information about the letters that make up this word. There are two conditions: Two different reflections should not alter the word. Try these two reflections on a word, say on SOLUTION, to make sure you un￾derstand the problem. 2. “Devising a plan.” We have to find the connection between what we are given and what we have to find. Which letters of the alphabet satisfy each of the two conditions? Both conditions? Find a word that is not changed if it is reflected in a horizontal line. Find a word that is not changed if it is reflected in a vertical line. Formulate the exact conditions for this exercise; that is, state the letters that can be used and how they must be arranged. 3. “Carrying out the plan.” Find a word that satisfies the conditions given above. 4. “Looking back.” Are there other solutions? Problem 1.2. Find a word (written in standard capital letters) that reads the same forward and backward and is still the same forward and backward when rotated around its center 180◦. Your solution needs to appear in a standard dictionary of some language. Problem 1.3. Solve the following anagrams. The first three are places (in the ge￾ographical sense), and the fourth is a place in which you might live. All can be rearranged to form a single word. (a) NOVA CURVE; (b) NINE SLAP NAVY; (c) I HELD A HIP PAL; (d) DIRTY ROOM. Note: You may have to find out exactly what an anagram is. This is part of Polya’s ´ first point on the list. Problem 1.4. Suppose n teams play in a single game elimination tournament. How many games are played? An example of such tournaments are the various categories of the U. S. Open tennis tournament; for example, women’s singles. Note: Pay special attention to the first entry of Polya’s list: “Is it possible to ´ satisfy the condition?” Problem 1.5. Suppose you are all alone in a strange house. There are seven identical closed doors. The bathroom is behind exactly one of them. Is it more likely, less likely, or equally likely that you find the bathroom on the first try than on the third try? Why?