In the third line, you ask for input. But a name is a string, so you need raw_input. raw_input takes strings, input only takes numerical values.
Python 2.7 getting user input and manipulating as string without quotations
Nowhere in your code do you update the variable questions, which I am guessing is a counter. You have to update that whenever a question is asked, using question += 1.
Finally, your code at the end does not really make sense. Based off the code, it checks for whether or not it is a string, but then compares it to the answer regardless. The if statement needs to be within the try.
The else statement does not match any outer indentation.
Finally, because of the while True: your code will never exit the loop unless the answer is wrong. At the point the entire program terminates. I see what kind of program you are trying to write, but the parameters for random number generation have to be within some kind of a while question <= 10 loop. As of now, only two lines in the program are being affected by that first while loop.
EDIT: I am working on a good example code. Hopefully this answer will help until I can finish it.
EDIT: Here is code that shows how it works within a while loop.
import random
from random import randint
name = raw_input("Hi, what is your name?\n") # Asks for name
print "Hi " +name+ " let's get started!"
score_count = 0
question_count = 0 # creates counter
while question_count <= 10: # Everything MUST BE WITHIN THIS LOOP
# makes numbers and operator
first_number = randint(1,10)
second_number = randint(1,10)
oper = random.choice("+""-""*")
# determines the problem
if oper == "+":
answer = first_number + second_number
print first_number,second_number,oper
elif oper == "-":
answer = first_number - second_number
print first_number,second_number,oper
elif oper == "*":
answer = first_number*second_number
print first_number, second_number, oper
user_answer = int(raw_input("Your answer: "))
if user_answer != answer:
print 'Wrong answer! try again!'
user_answer = int(raw_input('Your answer: '))
if user_answer == answer: # exits the while loop when the correct answer is given
if question_count < 10:
print 'Well done! Now onto question number {0}'.format(question_count+1)
score_count += 1
elif question_count == 10:
print 'Well done! You are done!'
score_count += 1
else:
print 'Something is wrong.'
question_count += 1 # updates the variable
# GOES BACK TO THE BEGINNING UNTIL question_count IS GREATER THAN OR EQUAL TO 10
print "Your score was: {}".format(score_count)
Happy coding! and best of luck!