Grades 5-6 Video Solutions 2022-2022_5-6

Video Transcription

Question number eight. Julia has one long dry spaghetti noodle she needs to make smaller.  Every time she breaks one piece of spaghetti, it becomes three pieces as shown in the picture. Which of the following numbers of pieces can she not get?  First thing to note here is that every time one piece of spaghetti is broken, it becomes three pieces.  This is pretty obvious in the first picture, but we have to realize that in every single picture that follows as well.  So when this piece breaks, it's also going to become three pieces. So the total number of pieces of spaghetti can only increase by 3 minus 1 equals 2 pieces with each break.  So we go from one piece to three pieces, and then we go from three pieces to 1, 2, 3, 4, 5, or 5 minus 3 is 2. So we're increasing by 2 pieces with each break.  Since Julia started with one piece of spaghetti, each break will add 2 to the total number of pieces.  Therefore, the number of pieces of spaghetti at the end still has to be odd no matter what. 20 is an even number, so it's impossible to reach. Therefore, the answer is C.

Video Summary

Julia starts with one spaghetti noodle, and each break increases the pieces by 2, resulting in only an odd number of pieces. Since every break results in this consistent pattern of increasing by two, she can only reach odd numbers of noodles. Hence, an even number like 20 pieces cannot be achieved starting from one piece. Therefore, the answer is that 20 pieces is the number she cannot get.