Grades 5-6 Video Solutions 2023-2023_1-2

Video Transcription

Question 25. On a table there is a tower made of blocks numbered from 1 to 50. Emma builds a new tower in the following way.  She takes two blocks from the top of the original tower and puts them on the table as the base of the new tower.  She continues by taking the top two blocks from the remainder of the original tower and putting them on the top of the new tower as seen in the diagram.  Which of the following pairs of numbers are on adjacent blocks in the new tower?  We can follow a rule where we take each even number and then the number below it in the new tower is 1 less and the number above it is 3 less.  For example, when we have the number 50, the number below it is 49 and the number above it is 47. With this we can test out our different potential solutions.  When we have 28, we have 27 and 25 next to each other, so it will not be A. When we have 34, we have 33 and 31, so it is not B. When we have 26, we have 25 and 23, so not C.  D has two odd numbers next to each other, so that cannot be the answer. Finally, if we have 30, we have 29 below it and 27 above it, so the answer will be E, 27 and 30.

Video Summary

Emma builds a new tower by taking two blocks from the top of an original tower and placing them on the table, then repeatedly transferring the top two blocks of the remaining tower onto the new one. To determine which pairs of numbers are adjacent in the new tower, observe that each even number has the number below it as 1 less, and the number above it as 3 less. Testing various combinations, the only viable pair that fits this pattern is 27 and 30. Thus, the pair of numbers on adjacent blocks in the new tower is 27 and 30.

Keywords

tower

blocks

adjacent

numbers

pattern