Problem number 17. Tom has nine cards as shown. He puts the cards on the board so that each horizontal line and each vertical line contains three cards with three different shapes and three different numbers of shapes. He has already placed three cards as shown. Which card does he put on the gray square? Looking at the cards, we see that they have the shapes of a circle, triangle, or square, and that the numbers of shapes at the card are 3, 2, and 1. we'll use the process of elimination to figure out which tile needs to go on the shaded square. In each column and in each row, each shape can occur only once. So we need to look at the gray square and look at the row and at the column to see what shapes and number of shapes were already used. We see that in the same column there's already something with circles in it and there's something with triangles in the same row as the gray shape. So whichever tile this is, it will have to have squares on it. Now we need to figure out how many squares will be on this tile. It will not be two because you already have two of something both in the square and the column. So it could be one or three. Let's look at the column here and let's look at this place. Using a similar idea, we're going to look across in the row and also in the column and we see that the numbers one and two already occur. So this will have to be the number three. Now we know that a tile with two of a shape and three of a shape are already used in the column. That means that our gray square can only be a tile with one shape and we already know that this shape is a square. So the tile that goes here is the tile with one square, which is answer D.

card placement

shape puzzle

gray square

logic puzzle

answer D