Question

Write code in Python: explain with comments Starting with two one-digit positive integers a and b, consider the sequence in which the next number is the digit in the ones place of the sum of the previous two numbers. For example, if a = 1 and b = 1, the sequence is 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, … Write a function mystery(a, b) that returns the length of the sequence when the last two numbers repeat the values of a and b for the first time. For example, if a = 1 and b = 1, the function should return 62.

Answer 1

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Python code in text

def mystery(a,b):

#initialize resulting list with a,b
resultinglist=[a,b]
#store initial value of a
inita=a
#store initial value of b
initb=b
#keep computing while until termination condition is reached with break
while True:

#the new element is ones place of summation of a and b, ones place of x is obtained by x%10
newelement=(a+b)%10
resultinglist.append(newelement)
#next iteration is to be taken for the b and the new element
a = b
b = newelement
#when last 2 elements are inital a and initial b respectively, termination condition is reached
if resultinglist[len(resultinglist)-2]==inita and resultinglist[len(resultinglist)-1]==initb:

break

print("Sequence is:-")
print(resultinglist)
#len(resultinglist) gives the length of this list
return len(resultinglist)

print(mystery(1,1))
print(mystery(2,2))