Fermi estimation
How good are you at estimating? Do you agree that it is a skill worth acquiring?
Plus magazine article on The art of guessing
How good are you at estimating? Do you agree that it is a skill worth acquiring?
Plus magazine article on The art of guessing
Find 11 positive integers such that none of them add up to a multiple of 11, or prove that this cannot be done.
The above problem was posted on the FB page of the Coursera Introduction to mathematical thinking mooc.
To begin with I misunderstood the problem, however reading posts by other members of the group it became clear what the problem was and of how to proceed. This provided a very interesting experience of being in a virtual classroom.
I began the problem after my Japanese class on Tuesday night reading it on my iPhone in my car — please note that the car was stationary:) The final insight was provided by a fellow classmates posting several hours later as I got out of bed.
I am adding my attempt at understanding this problem below for the sake of interest. As discussed on the group I am looking at a smaller number to begin with ie showing the case for 3 positive integers:
a 
b 
c 
a+b 
a+c 
b+c 
a+b+c 

Remainder 
1 
1 
1 
2 
2 
2 
3 ≡ 0 (mod3) 
Remainder 
1 
1 
2 
2 
2 
3 
4 ≡ 1 (mod3) 
Remainder 
1 
2 
2 
3 
3 
4 
5 ≡ 2 (mod3) 
Remainder 
1 
2 
1 
3 
2 
3 
4 
Remainder 
2 
2 
2 
4 
4 
4 
6 ≡ 0 (mod3) 
Remainder 
2 
2 
1 
4 
3 
3 
5 
Remainder 
2 
1 
1 
3 
3 
2 
4 
Remainder 
2 
1 
2 
3 
4 
3 
5 
This starts on Monday and I am enrolled in order to refresh my skills.
Introduction to Mathematical Thinking