Ethan Brown’s magic squares
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Brady who makes the Numberphile videos has had a tartan based on the fibonacci sequence created for him:
You can read about why it was made at Brady’s blog entry.
It’s “printed” tartan, but does look very nice.
is one of my favourite numbers — http://www.numbergossip.com/153
http://relprime.com/onetwothree/ on Numbers Gossip
A recent post by Peter Rowlett at Aperiodical was on the purpose of teaching surds for GCSE. Although I’m sympathetic to those who ask what their use is for in later life I think that they serve a purpose and deserve their place on the curriculum.
What are the smallest possible magic squares? €6900 still to win! (≈ $8500)
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 