A lattice point is a point with integer coordinates such as (2,3). An object in the plane moves from one lattice point to another. At each step, the object may move one unit to the right, one unit to the left, one unit up, or one unit down. If the object starts at (0,0) and takes a 10-step path, how many different points could be the final point?

Guest Mar 27, 2015

#2**+10 **

I have a different answer from Geno because have made different assumptions.

I have assumed that steps can be retraced so to get (0,0) for instance you could just keep going one place left then one right, one left, one right etc

I don't think that you can get the ones I have been left out but you can think about it for yourself.

Let me see,

I have

1 at the origin,

4*5 on the rest of the axes = 20

25 in the 1st quad so that is 100 in all four quads

1+20+100=121

Melody
Mar 28, 2015

#1**+5 **

We can count them all; let's first consider only those created by moving to the right and up.

We could end at these points (10,0), (9,1), (8,2), ..., (2,8), (1,9), and (0,10). These are 9 points in the first quadrant and 2 points on the axes.

In each quadrant, we get 9 points (for a total of 36 points) plus 4 more points for the axes. Total = 40 points.

geno3141
Mar 28, 2015

#2**+10 **

Best Answer

I have a different answer from Geno because have made different assumptions.

I have assumed that steps can be retraced so to get (0,0) for instance you could just keep going one place left then one right, one left, one right etc

I don't think that you can get the ones I have been left out but you can think about it for yourself.

Let me see,

I have

1 at the origin,

4*5 on the rest of the axes = 20

25 in the 1st quad so that is 100 in all four quads

1+20+100=121

Melody
Mar 28, 2015