Grades 3-4 Video Solutions 2023-2023_3-4

Video Transcription

Problem number 17. Six beavers and two kangaroos are standing in a line. Among any three consecutively numbered animals, exactly one is a kangaroo.  Which of the following numbered animals is a kangaroo? Here is the line, and we have answer choices 1, 2, 3, 4, and 5.  The problem tells us that among any three consecutively numbered animals, exactly one is a kangaroo. So we will need to look at these numbers in chunks of three.  Starting with 1, 2, and 3, one of these has to be a kangaroo. If number 1 is a kangaroo, then the other two are beavers. Then we would look at numbers 2, 3, and 4,  and we already would have 2 and 3 being beavers, number 4 would be a kangaroo. Then from 3, 4, and 5, we have the one kangaroo, so number 5 would be a beaver.  Looking at 4, 5, and 6, number 6 would be a beaver, because we already have one kangaroo in that group.  And when we start looking at 6 and 7, we would need another kangaroo here for this group.  So 1 can't be a kangaroo because it would mean that there are more than two kangaroos in line. So that's not going to be the answer.  If in this first group of three, 2 is a kangaroo, then number 1 is a beaver, number 2 is a beaver. If we consider 2, 3, and 4, 4 is a beaver.  And when we get to 3, 4, and 5, 5 has to be the kangaroo. If we're noticing a pattern, the next two will be beavers,  so that in this group, this group, and this group, there's one kangaroo. But when we get to number 8, that would have to be another kangaroo. So number 2 is also not a kangaroo.  So in this first group, number 3 has to be the kangaroo. There's beaver, beaver. Then remembering our pattern, to have one kangaroo in the group of 3 consisting of 2, 3, and 4,  there has to be a beaver here. And then looking at the group of 3, 4, and 5, there has to be a beaver here. By the time we're looking at 4, 5, and 6, we need another kangaroo.  But then we're going to have two beavers here. So the kangaroos are going to be at positions 3 and 6. And in the answer choices, we have 3.  We don't have 6 as an answer, so the answer is C.

Video Summary

The problem involves arranging six beavers and two kangaroos in a line such that among any three consecutively numbered animals, exactly one is a kangaroo. Analyzing the sequence and the constraints, the solution identifies that the kangaroos must occupy certain positions for the condition to hold true consistently. The video deduces that kangaroos are positioned at number 3 and number 6. Among the provided answer choices, only position 3 is listed. Therefore, the identified kangaroo position that satisfies the condition and aligns with the choices is number 3, which corresponds to answer choice C.

Keywords

beavers

kangaroos

sequence

positions

constraints