Solve it Sunday: Forty-Eight

Solve it Sunday: Forty-Eight

This week’s puzzle might take a little bit of math to solve, but it shouldn’t be too hard if you passed basic math classes. You’ll also need to know what square numbers mean…

I recommend grabbing a piece of paper and a pencil, and probably a calculator. Always good to have those around.

Many numbers, particlarly in the lower orders, can make a good claim for being of particular interest. It is in the realm of square numbers, that 48 is of special curiosity. If you add 1 to it, you get a square number
[48 + 1 = 49 = 7 x 7], and if instead you halve it and add 1 to the result, you get a different square number [48/2 = 24) + 1 = 25 = 5 x 5]. Individually, the two conditions are trivially common, but taken together this way, they are less so.

In fact, 48 is the smallest number to satisfy both conditions. Can you find the next smallest to do so?

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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?

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?

Solve It Sundays: Bodies in Motion

Solve It Sundays: Bodies in Motion

So before I get into the puzzle, I wanted to introduce a new segment I wanted to start. I bought a book a few years ago called Einstein’s Puzzle Universe and I really enjoyed trying to solve the riddles, and I thought some of you would too.

Now you’re probably thinking, OH, it’s Einstein, there’s no way I can solve his riddles, he was a genius. Well that may be true for some of the riddles, but most of them can be solved with a bit of applied brain power! Good luck with them, and let me know what you think, or if you think you know the answers, let me know!

I WILL ADD THE ANSWERS IN THE COMMENTS SECTION, SO DON’T SCROLL DOWN THERE IF YOU DON’T WANT THE ANSWERS.

We are used to the idea, that it is possible to sit still, and pass time in a motionless manner. But this amazing planet of ours is very far from static. At all times, we are hurtling through the gulfs of space at astonishing velocities.

It may seem to casual thought that from the Sun’s viewpoint, all of Earth’s population is moving at the same speed. After all, our planet revolves around it at a steady 30km per second – anticlockwise, if we are looking from above the North Pole. However, there is another factor to consider. The Earth spins on its axis as it rotates, at a speed of around 28km per minute, if you are at the equator.

You know, of course, that from the surface of the planet, the Sun appears to rise in the east. So, are you moving more swiftly during the day, or at night?

I’ve found the best way to solve some of these puzzles is to imitate them, at least to a certain extent. Obviously you don’t have a planet in your back pocket, but I’m sure you have a few roundish shaped objects laying around you can use.

Let me know in the comments if you figured out the answer, and remember, DON’T SCROLL PAST THIS UNTIL YOU’VE SOLVED IT, OR HAVE GIVEN UP. Spoiler warning below.

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