Crazy Products
Number Theory
Level
4
If seven consecutive numbers are chosen from 1 to 50, how many products ends with at least two zeros?
The answer is 20.
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1 solution
In order to make 2 zeros at the end, we need 100 as a factor which is equal to 2 2 × 5 2
( 4 − 1 0 ) , ( 5 − 1 1 ) , ( 9 − 1 5 ) , ( 1 0 − 1 6 ) , ( 1 4 − 2 0 ) , ( 1 5 − 2 1 ) , ( 1 9 − 2 5 ) , ( 2 0 − 2 6 ) , ( 2 4 − 3 0 ) , ( 2 5 − 3 1 ) ,
( 2 9 − 3 5 ) , ( 3 0 − 3 6 ) , ( 3 4 − 4 0 ) , ( 3 5 − 4 1 ) , ( 3 9 − 4 5 ) , ( 4 0 − 4 6 ) , ( 4 4 − 5 0 ) = 1 7 p o s s i b l e p r o d u c t s