mediummath

An athlete is able to jump FOREVER. However, every time that she jumps she gets a bit more tired, and every jump goes 1/2 as far as her prior jump. Now, for her very first jump, she goes 1/2 of a foot. On her second jump, she goes 1/4 of a foot, and so on and so forth.

The athlete will never reach one foot because they only ever jump half of the remaining distance

Why this works

This riddle cleverly plays with the concept of an infinite series. The athlete starts with a jump of 1/2 foot, and each subsequent jump is half of the previous one: 1/4 foot, 1/8 foot, and so on. While she can continue jumping forever, the total distance she covers is a series that converges to 1 foot but never actually reaches it. This illustrates a fascinating aspect of mathematics called limits, where you can get infinitely close to a value without ever fully attaining it.

Common Wrong Answers

“The athlete will reach one foot after two jumps.”

This is incorrect because the athlete jumps half as far with each successive jump, meaning she will only cover 1/2 foot on the first jump and 1/4 foot on the second jump, never actually reaching one full foot.

“The athlete will eventually reach two feet.”

This is wrong because the riddle specifies that with each jump the distance is halved, meaning she will never reach any whole number distance, including two feet.

“The athlete will reach one foot after an infinite number of jumps.”

While it's true that an infinite series of jumps can get closer to one foot, the athlete will never actually reach or exceed one foot, as each jump continues to be half of the previous jump.

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