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A Primary School Math Problem (Olympiad)
You can use enumeration, which is a bit troublesome. Is there an easier way? (Racking one's brains, suddenly my eyes shine) The topic is to cross out the numbers. Why can't we think backwards-add numbers? Step 1: put the numbers 1999, 1998, 1997 in front, because the smaller number is put in front, there is only one way to put it; Step 2: Add 997, which can be placed before 1997, after 1997, after 1998 and after 1999 respectively. Step 3: According to the four situations in step 2, 998 can only be placed after 997, and there can be 4, 3, 2 and 1 arrangements respectively. So far, the five numbers 997, 998, 1997, 1998 and 1999 have been put away. Step 4: According to the 10 pendulum in step 3, 98 can be placed in any position, that is, in the 10 pendulum, 98 has 6 pendulums. A * * * has 10*6=60 (species), that is, * * * has 60 different strokes.