benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / How many paths are there from A to B on the lines of the grid shown, if every step must be up or to the right?[asy]size(3cm,3cm);int w=6;int h=3;int i;for (i=0; i<h; ++i) draw((0,i…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

How many paths are there from AA to BB on the lines of the grid shown, if every step must be up or to the right?[asy]size(3cm,3cm);int w=6;int h=3;int i;for (i=0; i<h; ++i){ draw((0,i) -- (w-1,i));}for (i=0; i<w; ++i){ draw((i, 0)--(i,h-1));}label("BB", (w-1,h-1), NE);label("AA", (0,0), SW);[/asy] For example, here is one such valid path highlighted in blue: [asy] size(3cm,3cm); int w=6; int h=3; int i; for (i=0; i<h; ++i){ draw((0,i) -- (w-1,i)); }for (i=0; i<w; ++i){ draw((i, 0)--(i,h-1)); } label("BB", (w-1,h-1), NE); label("AA", (0,0), SW); draw((0,0)--(1,0), blue+1.5); draw((1,0)--(1,1), blue+1.5); draw((1,1)--(2,1), blue+1.5); draw((2,1)--(3,1), blue+1.5); draw((3,1)--(4,1), blue+1.5); draw((4,1)--(4,2), blue+1.5); draw((4,2)--(5,2), blue+1.5); [/asy]
Plain-text mathematical notation (without MathML)
How many paths are there from A to B on the lines of the grid shown, if every step must be up or to the right?[asy]size(3cm,3cm);int w=6;int h=3;int i;for (i=0; i<h; ++i){ draw((0,i) -- (w-1,i));}for (i=0; i<w; ++i){ draw((i, 0)--(i,h-1));}label("B", (w-1,h-1), NE);label("A", (0,0), SW);[/asy]
For example, here is one such valid path highlighted in blue:
[asy]
size(3cm,3cm);
int w=6;
int h=3;
int i;
for (i=0; i<h; ++i){ 
draw((0,i) -- (w-1,i));
}for (i=0; i<w; ++i){ 
draw((i, 0)--(i,h-1));
}
label("B", (w-1,h-1), NE);
label("A", (0,0), SW);

draw((0,0)--(1,0), blue+1.5);
draw((1,0)--(1,1), blue+1.5);
draw((1,1)--(2,1), blue+1.5);
draw((2,1)--(3,1), blue+1.5);
draw((3,1)--(4,1), blue+1.5);
draw((4,1)--(4,2), blue+1.5);
draw((4,2)--(5,2), blue+1.5);
[/asy]
Original LaTeX notation
How many paths are there from $A$ to $B$ on the lines of the grid shown, if every step must be up or to the right?[asy]size(3cm,3cm);int w=6;int h=3;int i;for (i=0; i<h; ++i){ draw((0,i) -- (w-1,i));}for (i=0; i<w; ++i){ draw((i, 0)--(i,h-1));}label("$B$", (w-1,h-1), NE);label("$A$", (0,0), SW);[/asy]
For example, here is one such valid path highlighted in blue:
[asy]
size(3cm,3cm);
int w=6;
int h=3;
int i;
for (i=0; i<h; ++i){ 
draw((0,i) -- (w-1,i));
}for (i=0; i<w; ++i){ 
draw((i, 0)--(i,h-1));
}
label("$B$", (w-1,h-1), NE);
label("$A$", (0,0), SW);

draw((0,0)--(1,0), blue+1.5);
draw((1,0)--(1,1), blue+1.5);
draw((1,1)--(2,1), blue+1.5);
draw((2,1)--(3,1), blue+1.5);
draw((3,1)--(4,1), blue+1.5);
draw((4,1)--(4,2), blue+1.5);
draw((4,2)--(5,2), blue+1.5);
[/asy]

level

Level 3

type

Counting & Probability

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
bfd999d0-69c5-5a3a-862c-2a8b304c9454
task_key
counting~5fand~5fprobability--test--bfd999d0-69c5-5a3a-862c-2a8b304c9454
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import