A plan that failed
- I am nine, she smiled.
- That’s great, I replied, turning to the sports page. I am 91.
- Do you know the cube of 2? she persisted.
- 8, I answered sub-consciously.
- Won’t do then, she said disappointed.
- Why not?
- The remainder when I divide it by 9 has to be 1.
- I see, I said, reading about the local basketball team. They had lost again.
- Do you know the cube of three, she asked innocently.
- Yes, but you won’t like it. Its remainder with 9 is not 1.
- I can never do this, she said.
- What? I asked, putting down the paper.
- I have to add up all numbers between 2 and 8 whose cube gives 1 when divided by 9.
- Who would give such a stupid task, I asked irritated.
- You did, she sighed. You wanted to read the paper in peace I guess.
- So much for that plan, I half smiled.
Being 91 and the proud owner of Calc spreadsheet I tried to solve her problem as if I was her. In other words I tried to find the sum of all numbers from 2 to 90 whose cube when divided by 91 gave 1 as the remainder.
It was a no-brainer. Here are my sheets.
When I showed it to her she refused to put down her comic book to give it a glance.
My second disappointment followed shortly thereafter. Project Euler asks for the sum for people who are 13082761331670030 years old.
My spreadsheet approach required no thinking, my area of expertise. Euler’s question left me feeling 99% inadequate and 1% curious on how on earth the problem can be solved.
January 10th, 2010 at 9:55 am
I’ve been working on this myself. There are interesting features about numbers 91 and 13082761331670030 that I believe can be exploited. Not sure yet. I’m on the clock.