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Grades are a consequence: why strong students need to be fluent, present, and bold
Picture a junior we'll call Johnny. He has never had much trouble in school. He gets A's, he does his homework, and when his first big physics test came up this fall, he prepared the way he always does. He reread the chapter, redid the homework problems, and made a...
I have to admit I am somewhat older than a middle-schooler. I am getting the answer “no”. Is that correct?
Yes, but without a proof, that wouldn’t get much credit. 😉
Fair enough. To be the sum of a formidable number and a successful number, 2005 will have to be the sum of a subset of the following terms — each chosen 0 or 1 time:
1 4 16 64 256 1024
1 6 36 216 1296
We cannot choose both 1024 and 1296, because that exceeds 2005.
Hence the maximum we can achieve is the sum of 1 4 16 64 256 1 6 36 216 1296
But that maximum is less than 2005.
QED (quite easily done).
Complete, direct, concise: I don’t know how I could improve on that! Well done.
…and thanks for the inspiration and reminder to start posting again now that I’m back from vacation.