2017 AMC 10B Problems/Problem 6: Difference between revisions
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==Problem== | ==Problem== | ||
What is the largest number of solid <math>2\text{-in} \times 2\text{-in} \times 1\text{-in}</math> blocks that can fit in a <math>3\text{-in} \times 2\text{-in}\times3\text{-in}</math> box? | |||
<math>\textbf{(A)}\ | <math>\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math> | ||
==Solution== | ==Solution== | ||
We find that the volume of the larger block is <math>18</math>, and the volume of the smaller block is <math>4</math>. Dividing the two, we see that only a maximum of four <math>2</math> by <math>2</math> by <math>1</math> blocks can fit inside the <math>3</math> by <math>3</math> by <math>2</math> block. Drawing it out, we see that such a configuration is indeed possible. Therefore, the answer is <math>\boxed{\textbf{(B) }4}</math>. | |||
{{AMC10 box|year=2017|ab= | ==Video Solution== | ||
https://youtu.be/lgdWiCz6M3c | |||
~savannahsolver | |||
==Video Solution by TheBeautyofMath== | |||
https://youtu.be/XRfOULUmWbY | |||
~IceMatrix | |||
==See Also== | |||
{{AMC10 box|year=2017|ab=B|num-b=5|num-a=7}} | |||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 19:04, 1 May 2021
Problem
What is the largest number of solid 
blocks that can fit in a 
box?
Solution
We find that the volume of the larger block is 
, and the volume of the smaller block is 
. Dividing the two, we see that only a maximum of four 
by by 
blocks can fit inside the 
by by block. Drawing it out, we see that such a configuration is indeed possible. Therefore, the answer is 
.
Video Solution
~savannahsolver
Video Solution by TheBeautyofMath
~IceMatrix
See Also
| 2017 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America. 
