1. you are an amazingly successful hotelier; one of your properties is "chez four-thirteen". suppose there are 8 distinguishable hotel rooms (numbered 101, ), each with maximum occupancy of 4 people. a bus comes in with anywhere from 1 to 32 (distinguishable) people, but you do not know exactly how many. while waiting, you decide to calculate (making use of your uiuc math 413 education) the number of possible ways the people on the bus can spend the night in those hotel rooms so you can make a welcome sign. determine this number. use a computer to express the answer with all the digits (e. g., 31415926535897932384626433832795); write down for your check-in clerk the order of magnitude (e. g., 1032). i recommend python to do the computation.

Nicolo paganini's numbers 1184 and 1210 are amicable. the proper divisors of 1184 are 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, and 592. the proper divisors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, and 605. use the definition of amicable (friendly) numbers to show that they are indeed amicable. which of the folowing statement uses the definition of amicable numbers to show that 1184 and 1210 are indeed amicable? o a. o b. ° c. the sum of proper divisors of 1184 is 1210 and the sum of proper divisors of 1210 is 1184 the sum of proper divisors of 1184 is greater than 1210 and the sum of proper divisors of 1210 is greater than 1184 the sum of proper divisors of 1184 is less than 1210 and the sum of proper divisors of 1210 is less than 1184