Quandaries
and Queries 

Hi My name is Samuel and I am a secondary student. My question is the following: If we add one 1 at the beginning and at the end of a number, this number is increased by 14789. What is the sum of the digits of the number?. Many thanks for your help. 

Samuel, I am going to do a similar problem.
I think that the number must have 3 digits so that when I add a 1 to each end I get 1 5 digit number. Lets say the number is pqr, then adding a 1 to each end gives 1pqr1. The problem says that 1pqr1 is 15185 more than pqr, that is
From above 5 + r has a units digit of 1 so r = 6.
Continuing to add, 5 + 6 = 11 and 8 + 1 + q has a units digit of 6. Thus q = 7.
In a similar fashion p must be 5 so the number you started with was 576. Penny
