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18 June, 15:14

A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?

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  1. 18 June, 15:42
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    Answer: No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

    Step-by-step explanation:

    If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

    Changing to any other amount just gets farther away from the goal.

    A system of equations yields no solution of integers.

    x + y = =100

    19x - 17y = 101

    You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!
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