bonanova Posted November 2, 2010 Report Share Posted November 2, 2010 Our grocer got a new shipment of oranges. Tired of he held a quick clearance sale for his triangle oranges, and arranged his new stock into a square pyramid. That is, the topmost orange sat on a layer of four [2x2], which rested on a layer of nine [3x3] and so on until the final orange was found to exactly complete the bottom-most square layer of dimensions [nxn]. Of course, he built his square pyramid from the bottom up. Describing from top down just seemed more convenient. But then came the inevitable encounter with the cell phone shopper's cart! Amazingly, thought the grocer, and it was in fact amazing, as you'll discover, the fallen oranges became a new square array, with every orange touching the floor. Just one question remains. What was n?. Quote Link to comment Share on other sites More sharing options...
0 araver Posted November 2, 2010 Report Share Posted November 2, 2010 n=24. 24*25*49 /6 = 70*70. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 2, 2010 Report Share Posted November 2, 2010 Either 4 or 21 For n=4 the sum of the squares for 1, 2, 3 & 4 is 25, which would leave a 5 x 5 square when all of the oranges touch the floor. For n=21, the sum of the squares for the numbers 1 thru 21 is 841, which would leave a 29 x 29 square when all of the oranges touch the floor. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 2, 2010 Report Share Posted November 2, 2010 Made a mistake in my program to sum the squares n = 24 Sum of squares 1 thru 24 = 4900 or 70 squared Quote Link to comment Share on other sites More sharing options...
0 araver Posted November 2, 2010 Report Share Posted November 2, 2010 Imhere, please use spoilers. Instructions can be found in the red box when you reply: "TIP: You can hide your answer in "Spoiler" so that others don't see it if they choose so. Simply click on the blue "Spoiler" button, write the visible spoiler title and in the next line write the text that should be masked." Thank you Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 2, 2010 Report Share Posted November 2, 2010 There was 1 orange... The guy freaked out and then was surprised for nothing...the shopper got very confused and left. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 2, 2010 Report Share Posted November 2, 2010 (edited) 24 Edited November 2, 2010 by Bill West Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 2, 2010 Report Share Posted November 2, 2010 (edited) 24, but not the first Just one question remains. What was n?. Edited November 2, 2010 by xucam Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 7, 2011 Report Share Posted January 7, 2011 Our grocer got a new shipment of oranges. Tired of he held a quick clearance sale for his triangle oranges, and arranged his new stock into a square pyramid. That is, the topmost orange sat on a layer of four [2x2], which rested on a layer of nine [3x3] and so on until the final orange was found to exactly complete the bottom-most square layer of dimensions [nxn]. Of course, he built his square pyramid from the bottom up. Describing from top down just seemed more convenient. But then came the inevitable encounter with the cell phone shopper's cart! Amazingly, thought the grocer, and it was in fact amazing, as you'll discover, the fallen oranges became a new square array, with every orange touching the floor. Just one question remains. What was n?. i have concluded that we need to solve the equation n(n+1)(2n+1)/6=t^2, where t is a natural no. however i am unable to slove further, some hints of approaching the problem plz. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 7, 2011 Report Share Posted January 7, 2011 580 Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 8, 2011 Report Share Posted January 8, 2011 Imhere, please use spoilers. Instructions can be found in the red box when you reply: "TIP: You can hide your answer in "Spoiler" so that others don't see it if they choose so. Simply click on the blue "Spoiler" button, write the visible spoiler title and in the next line write the text that should be masked." Thank you i have concluded that we need to solve the equation n(n+1)(2n+1)/6=t^2, where t is a natural no. however i am unable to slove further, some hints of approaching the problem plz. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 10, 2011 Report Share Posted January 10, 2011 I think the real question is - Why was the grocer amazed? that 4900 oranges were needed to make the pyramid. Didn't he know that 4900 was a perfect square? Quote Link to comment Share on other sites More sharing options...
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bonanova
Our grocer got a new shipment of oranges.
Tired of he held a quick clearance sale for his triangle
oranges, and arranged his new stock into a square pyramid. That is, the
topmost orange sat on a layer of four [2x2], which rested on a layer of nine
[3x3] and so on until the final orange was found to exactly complete the
bottom-most square layer of dimensions [nxn]. Of course, he built his square
pyramid from the bottom up. Describing from top down just seemed more
convenient.
But then came the inevitable encounter with the cell phone shopper's cart!
Amazingly, thought the grocer, and it was in fact amazing, as you'll discover,
the fallen oranges became a new square array, with every orange touching
the floor.
Just one question remains. What was n?.
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