Grades 5-6 Video Solutions 2021-video 2021 5-6/30

Video Transcription

Alright, and now for the last problem in this year's Math Kangaroo. Number 30, there are rectangular cards divided into four equal cells with different shapes.  We have a square, a star, a circle, and a triangle drawn in each cell. So cards can be placed side by side only if the same shapes appear in adjacent cells on their common side.  Nine cards are used to form a rectangle as shown in the figure. One of the following cards was definitely not used to form this rectangle.  Okay, so we can eliminate cards based on if they can be placed adjacent to the given card.  So again, this is one of those not problems, so just let's try and eliminate the ones that can be used to form this rectangle. So what if we want to match a card over here?  Well, we see a triangle and a square on the right column here, so a triangle and a square must be on the left column here.  It doesn't matter what order they are, it doesn't say that they have to be in the same order. It just says that the same shapes have to appear in adjacent cells on the common side.  So if we find something that is a square and a triangle on the left side, we can eliminate those.  Well, D has a square and a triangle on the left side, and B also has a square and a triangle on the left side. Okay, great, we can eliminate those two.  Okay, what if we want to match below over here? Well, if we want to match below, then the top should have the star and the square.  Well, let's see which ones have the star and the square. A has a star and a square. C has a star and a square. Okay, so that eliminates A and C, and now only E remains.  Just to check, we can't put E below it. This circle doesn't match up with the square.  We can't put E on the right-hand side. This star doesn't match up with the triangle, and so E cannot be used to form this triangle. The answer, therefore, is E.

Video Summary

The problem involves arranging nine rectangular cards with different shapes in each cell such that cards can only be placed adjacent if the shapes match on their common sides. The task is to identify which card was not used to form the given rectangle. By process of elimination, cards with matching shapes on the left or top were identified, narrowing down possibilities. After evaluating positioning compatibility, it was concluded that card E did not fit the criteria for placement, as neither its top nor side shapes matched with adjacent cards. Therefore, card E was not used.

Keywords

rectangular cards

shape matching

card elimination

adjacent placement

unused card