Would you have known immediately that the number 1729 is the sum of two cubes?
You think you’re so smart, but you’re no Ramanujan. He told Hardy that 1729 is the sum of two cubes in two ways: 13+123 and 93+103.
Also, I subjected my students to this 14-minute podcast about Hardy and Ramanujan.
One more “fair share” task for my 8th graders from Peter Liljedahl’s site because I like it and don’t want to work in the textbook as our students are taking the Smarter Balanced Tests this week.
Six years ago you made an investment with a friend – you bought a house together. It wasn’t only an investment, it was also a favor. Your friend didn’t have a place to live and didn’t have enough money to buy a house. So, you pooled your money and bought a $300,000 house for your friend to live in. You provided $50,000 for the down payment and your friend provided $25,000. Because of the size of the down payment it meant that the mortgage was relatively low – only $1000 a month – which your friend paid. During the six years all property tax payment were split evenly between you as were all major renovations and upgrades. Well, it is now six years later and your friend is getting transferred to Ontario. So, you have sold the house for $500,000 (the market has been good to you). There is still $200,000 outstanding on the mortgage. How will you split the $300,000 equity between you? Justify your decision.
A couple of solutions thus far: