Christmas trees
Christmas trees are planted in a rectangular array. Which is the taller tree, A or B?
Age
11 to 14
Challenge level
Problem
| Christmas trees are planted in a rectangular array of 10 rows and 12 columns. The farmer chooses the shortest tree in each of the columns and then marks the tallest of these 12 shortest trees with a letter A. Then the farmer chooses the tallest tree from each of the rows and marks the shortest of these 10 tallest trees with a letter B. Which is the taller tree, A or B? | Image
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Student Solutions
The following solution is from Xinxin, Tao Nan School, Singapore
Of the 12 shortest trees, A is the tallest. Nevertheless it is the shortest in its column.
Of the 10 tallest trees, B is the shortest. Nevertheless it is the tallest in its row.
The row where B is and the column where A is intersect at a tree. Let us call this tree C.
Now, C is definitely shorter than B because B is the tallest in C's row. In terms of height, C < B
And of course, A is definitely shorter than C because A is the
shortest in C's column.
In terms of height, A < C
If A < C and C < B then A < C
Thus A < B
So B is taller than A.