For the next questions we are going to develop some ideas about representing numbers using casino chips. Vegas uses chips of value 1, 5, and 25, colored respectively white, blue, and red. Reno uses chips of the same value and color, but you must always "color up" to have the smallest number of chips. (For example, if you have six white chips you would have to ex- change five of them for a blue chip.) (a) In each system, find all the different ways you can represent the number 31. (b) We can even write numbers based on these systems of casino chips. Say that abcReno means you have a red chips, b blue chips, and c white chips. (For example, 123Reno means 1 red chip worth 25, 2 blue chips worth 5 each, and 3 white chips worth 1 each, for a total of 38.) What numbers are expressed by 321Reno, 444Reno, and 031Reno? (c) Write the numbers 14, 36, and 101 as Reno numbers. (d) What is wrong with writing 073Reno? (e) What would be problematic about writing Vegas numbers like this? Page 1