Very Fun Problem

Level 2

Let p p be every single digit of pi multiplied together (e.g. 3 × 1 × 4 × 1 × 5... 3 \times 1 \times 4 \times 1 \times 5... ), but for every seven, instead of multiplying, divide. What is p p divided by 7,893,797,430?


The answer is 0.

Finn Hulse by Finn Hulse , 21, USA

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2 solutions

Kenny Lau
Dec 3, 2014

The numerator surely contains 0, but so does the denominator, which makes p undefined. Therefore, this problem is incorrect.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Lewis Tough
Jan 26, 2014

Pi is infinite, so the occurrences of each digit are infinite too. Infinity/Infinity is 0. Dividing 0 by anything is 0, which is our final answer.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Well... Not exactly... As soon as you reach your first zero in pi, everything turns to zero. The whole problem is a trick. Multiplying, dividing, no matter what you do, you can't get anything but zero. So everything else is just a trick.

Finn Hulse - 7 years, 4 months ago

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Troll problem. :D

Sharky Kesa - 7 years, 1 month ago

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Yeah, haha.

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse – 7,893,797,430 was this number out of the blue? Thanks

Spock Weakhypercharge - 7 years, 1 month ago

One would still have to check that the first zero indeed happens when multiplying, and not when dividing.

Daniel Liu - 7 years ago

Suppose both are equally valid.

Lewis Tough - 7 years, 4 months ago

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Yeah, but anything times infinity is infinity. Not just zero.

Finn Hulse - 7 years, 4 months ago

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Infinity/Infinity is 0 I believe?

Lewis Tough - 7 years, 4 months ago

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@Lewis Tough – But that would imply that having no infinities is actually infinite. You bring up a very interesting point: Which is more powerful? Infinity or zero? When you multiply them, do you get infinity or zero? But as for infinity/infinity: When you have, say, 3 infinities, do you have still an infinite amount? Yes. That is why anything times infinity is infinity.

Finn Hulse - 7 years, 4 months ago

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@Finn Hulse – To reduce the confusion, I believe that infinity does not exist. So anything divided by zero is not defined, so division by zero is not defined. Hope it helps!

Satvik Golechha - 7 years, 1 month ago

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@Satvik Golechha – Yes, you are correct.

Finn Hulse - 7 years, 1 month ago

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