SOLUTION: A child wishes to build up a triangular piles of toy bricks so as to have one brick In the top flow, 2 in the second, 3 in the third and so on . if he has 100 bricks, how many rows

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Question 1161225: A child wishes to build up a triangular piles of toy bricks so as to have one brick In the top flow, 2 in the second, 3 in the third and so on . if he has 100 bricks, how many rows can complete and how many bricks has he left
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

A triangular pile with n rows of bricks requires  1 + 2 + 3 + . . . + n =  bricks  (= the sum of the first n natural numbers).


The table is


n  (rows)    1   2   3    4     5     6     7     8     9    10    11   12   13

N (bricks)   1   3   6   10    15    21    28     36   45    55    66   78   91


So, having 100 bricks, the child can build 13-stores pyramid.


He (or she) will use 91 bricks, and 100-91 = 9  bricks will left.

Solved.

-----------------

If you want to know the basics for it, it is about arithmetic progressions.

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions (*)
in this site.

By the way, you will find a picture for your problem in the lesson marked (*) in the list.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.




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