Problem 44307. The glass half full

Created by HH

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Identical glasses are placed in a triangular tower structure, such that the top level (L = 1) comprises one glass, the next level down (L = 2) comprises three glasses, the next level down (L = 3) comprises six glasses, and so on.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Follow the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://imgur.com/a/j9ZZa\"><w:r><w:t>link</w:t></w:r></w:hyperlink><w:r><w:t> to see a diagram shows the first three levels. The glasses in each levels are represented by the blue circles, while the yellow circles represent the positions of the glasses in the next higher level.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Water is poured into the top glass at a constant volumetric flow rate. When the glass is filled, the water starts spilling over and into the glasses below. Note that</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>water only spills outward</w:t></w:r><w:r><w:t> , meaning that at some point, some glasses will remain empty.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given the volume of a glass in liters, v, the volumetric flow rate in liters per second, u, and an integer, L, representing a level in the glass structure, return the total number of glasses in that level, g, the number of glasses in that level that will be filled with water, f, and the time, in seconds, it would take to fill all \"fillable\" glasses in that level, t, starting with no water in any of the levels.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Input: v = 0.25, u = 0.1, L = 2</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Output: g = 3, f = 3, t = 10</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Identical glasses are placed in a triangular tower structure, such that the top level (L = 1) comprises one glass, the next level down (L = 2) comprises three glasses, the next level down (L = 3) comprises six glasses, and so on.Follow the <a href = "https://imgur.com/a/j9ZZa">link</a> to see a diagram shows the first three levels. The glasses in each levels are represented by the blue circles, while the yellow circles represent the positions of the glasses in the next higher level.Water is poured into the top glass at a constant volumetric flow rate. When the glass is filled, the water starts spilling over and into the glasses below. Note that water only spills outward , meaning that at some point, some glasses will remain empty.Given the volume of a glass in liters, v, the volumetric flow rate in liters per second, u, and an integer, L, representing a level in the glass structure, return the total number of glasses in that level, g, the number of glasses in that level that will be filled with water, f, and the time, in seconds, it would take to fill all "fillable" glasses in that level, t, starting with no water in any of the levels.Example:Input: v = 0.25, u = 0.1, L = 2Output: g = 3, f = 3, t = 10

Identical glasses are placed in a triangular tower structure, such that the top level (L = 1) comprises one glass, the next level down (L = 2) comprises three glasses, the next level down (L = 3) comprises six glasses, and so on.

Follow the <https://imgur.com/a/j9ZZa link> to see a diagram shows the first three levels. The glasses in each levels are represented by the blue circles, while the yellow circles represent the positions of the glasses in the next higher level.

Water is poured into the top glass at a constant volumetric flow rate. When the glass is filled, the water starts spilling over and into the glasses below. Note that *water only spills outward* , meaning that at some point, some glasses will remain empty.

Given the volume of a glass in liters, v, the volumetric flow rate in liters per second, u, and an integer, L, representing a level in the glass structure, return the total number of glasses in that level, g, the number of glasses in that level that will be filled with water, f, and the time, in seconds, it would take to fill all "fillable" glasses in that level, t, starting with no water in any of the levels.

Example:

Input: v = 0.25, u = 0.1, L = 2

Output: g = 3, f = 3, t = 10

Solve

Solution Stats

667 Solutions
244 Solvers

Last Solution submitted on Oct 01, 2022

Last 200 Solutions

Problem Comments

Solution Comments

Solution 1656065

2 Comments

2 Comments

Chris Breshike on 22 Oct 2018

could someone explain the different between g and f in this problem? don't all the glasses get filled in the bottom level?

HH on 23 Oct 2018

Chris, the problem states (in bold font) that "water only spills outward" and therefore not all glasses are necessarily filled.

Problem Recent Solvers244

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44307. The glass half full

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers244

Suggested Problems

More from this Author35

Problem Tags

Community Treasure Hunt

Problem 44307. The glass half full

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers244

Suggested Problems

More from this Author35

Problem Tags

Community Treasure Hunt

Players