Solve it Sundays: Submersible

Solve it Sundays: Submersible

By now, your weekend is probably pretty close to done, but that doesn’t mean you shouldn’t stop relaxing.

Take a seat on the couch and try to solve this week’s riddle.

There are many pressing concerns when one is in a submarine, whether it is a time of war or not. However, one of the most important is for the captain to ensure that his boat not be permitted to rest on the bedrock of the ocean floor, even for a moment. Such an event may well prove fatal for the entire crew.

Can you say why?

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Solve it Sundays: An Exercise in Logic

Solve it Sundays: An Exercise in Logic

Hey everyone. This week’s riddle is a bit easier for you, but it’ll for sure make you think.

The English mathemitician and author Lewis Caroll devised a series of excellent logical problems designed to illustrate and test deductive reasoning. Several statements are given below. You may assume — for the duration of this problem — that they are absolutely true in all particulars. From that assumption, you should be able to provide an answer to the question that follows.

I dislike things that cannot be put to use as a bridge.

Sunset clouds are unable to bear my weight.

The only subjects I enjoy poems about are things which I would welcome as a gift.

Anything which can be used as a bridge is able to bear my weight.

I would not accept a gift of a thing I disliked.

Would I enjoy a poem about sunset clouds?

Solve it Sundays: Absolutely Nothing

Solve it Sundays: Absolutely Nothing

We are back for another Solve it Sundays, and this one I didn’t find too tricky. Good luck! and as always, the answers are in the comments.

 

It is tempting, soothing even, to think of mathematics as a perfect edifice of logic and order. The truth however is that it is an art as well as a science, and it has places where absolutism breaks down.

For this example, we will show that 0 = 1. Firstly, however, I should point out that when adding a series of numbers, the associative law says that you may bracket the sums as you like without any effect.

1+2+3 = 1+ (2+3)= (1+2) + 3.

So, with that established, consider adding an infinite number of zeroes. No matter how much nothing you gather, you will still always have nothing.

0 = 0+0+0+0+0+…

Since 1-1 = 0, you can replace each zero in your sum, like so:

0 = (1-1)+(1-1)+(1-1)+(1-1)+(1-1)+…

From the associative law, you may arrange the brackets in your sum as you see fit. Which means:

0 = 1+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+…

However, as established, (-1+1) = 0, so this sequence can also be stated as:

0 = 1+0+0+0+0+0+…

Or, for simplicities sake:

0 = 1

Something is clearly incorrect. But what?

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