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# Christmas Trees

##### Age 11 to 14 Challenge Level:

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.