A mathematician was bored during a long train ride from Upstate New York to New York City. Having a little notebook and a pencil always handy, she began to scribble the following:
The Task:1. What is the mathematician investigating here?
2. Can you find patterns when you continue her investigation for 2-digit numbers? For 3-digit numbers? For numbers of any amount of digits?
3. The differences above (297 and 792) are divisible by 99. What about the differences of reversed squares for any 2-digit number? What about 3-digit numbers? What about numbers with any amount of digits?
Be sure to follow all the standard POTU Write-Up guidelines.
DUE:
Blue: Tuesday, Dec. 11th
Red: Wednesday, Dec. 12th
Green: Wednesday, Dec. 12th
5 comments:
Do you answer the question by looking at the second number?
why would a person start at that position?
You can start with any 2-digit number and experiment from there, keeping track of your results. The idea is to find patterns like the mathematician did. Then try 3-digit numbers, again keeping track of your results. Does a pattern emerge?
do we have to add all the digits together (differences of reversed quareds) because they all seem to have a sum on 18, when a two digit number. And when a three digit number, they have a sum of 27...so is the pattern, that for every digit number added on, then sum of the differences of the reversed sqaures equal 9 times the amount of digits in a number?
Can you prove that statement?
41^2-14^2=1681-196=1485
1485=1+4+8+5=18
and
342^2-243^2=116964-59049=57915
57915=5+7+9+1+5=27
uhm..if you try any other number, I suppose it has the same pattern.
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