Vipin sends us the following question:

_+_+_+80+90=100 , no negetive number in the question.

There are multiple ways to solve this equation, but I have no idea if the ones I came up with are the ones the problem creator was looking for. That's okay. If you come up with a solution that works, it doesn't matter if it's "the right one."

For people reading this question, I'm about to propose a solution, so if you want to try to figure out a solution for yourself, do it now, before you read any further!

--- SOLUTIONS BELOW ---

The first thing I did to this was, I subtracted 80 and 90 from both sides of the equation, which turned it into:

_ + _ + _ = 100 - 80 - 90

_ + _ + _ = -70

If you don't mind, I'm going to replace those blanks with variables, because then I can talk about each individual blank by name:

a + b + c = -70, where a, b, and c are not negative.

I came up with a few possibilities; the first two use complex numbers.

Solution One

a = 0, b = -30 + i, c = -40 - i

I know, you'll be tempted to say, "Wait! -30 and -40 are negative numbers!" To which I reply, "No, -30 is part of the complex number -30 + i. Complex numbers are neither negative nor positive, so I have filled the blanks with numbers which are not negative."

Maybe you'd like to argue that the point is to not use the negative symbol at all. In which case, I give you solution #2:

Solution Two

a = 0, b = 30i², c = 40i²

I've used no negative symbols, but b and c evaluate to -30 and -40 respectively, giving the desired result.

Maybe you'd like to argue that you can't use negative symbols and you can't use expressions that evaluate to negative numbers. In which case, I would say, "Stop adding to the rules and find your own solution!" ;)

If you're willing to accept solution two, it opens up a boatload of possibilities, like using trig, or other functions:

Trig Solution

a = 0, b = 0, c = 70cos(180º)

If our readers aren't willing to accept any of these answers, please use the "Ask Professor Puzzler" link at the bottom of the page to suggest your own solution. Be sure to mention what blog post you're writing about! If we get any solutions we like, we'll add them to the bottom of the post.

Good morning Puzzling Friends! I have a puzzle for you all.

rinku sends us the following question: "How can we get one using the numbers 1 to 10 in the same order using the four operations?"

This is all we have for details on this puzzle. It is not clear, from the wording, whether parentheses are allowed.

For example, are you allowed to do things like this: 1(2 + 3 - 4) + 5... etc. If you can use parentheses, that simplifies the problem, I'm sure!

I'm curious to see how many different solutions we can come up with. Try doing it without parentheses, and if you can't solve it, try it with parentheses. Use the "Ask Professor Puzzler" link at the bottom of the page to submit your answer. 

I'll update this blog post with the first/best submissions, so make sure you check back next week to see what solutions have been shared!
 

The only solutions which were posted were variations on a single theme.

It occurred to me, as I looked at this, that each pair of successive integers had a difference of one (or negative one, depending on which way you do the subtraction). Thus, if we alternate adding and subtracting differences, we'll get the desired solution:

First we add 2 to -1.
Then we subtract 4 from 3.
Then we add 6 to -5.
Then we subtract 8  from 7.
Finally, we add 10 to -9.

-1 + 2 +3 - 4 - 5 + 6 + 7 - 8 - 9 + 10 = 1

The other solutions received were simply variations on the add and subtract differences concept, such as:

1 - 2 + 3 - 4 - 5 + 6 - 7 + 8 - 9 + 10 = 1.

Many other variations are possible.

Can you find a solution that includes operations besides addition and subtraction? Use the "Ask Professor Puzzler" link to give us your solution!

Mohamed from Maldives asks the following question: "Mr. Smith and his son are driving in a car. They get into an accident. Mr. Smith dies and his son rushed into the hospital and the surgeon said I cant operate on him because he is my SON. How is that?"

Hi Mohamed, this is an old, old riddle which is slowly disappearing from usage. Because of changes in society, people are becoming more and more likely to recognize the answer quickly. I'll explain what I mean in a minute, but first, the answer to your question:

The surgeon was his mother.

I first heard this riddle when I was a child in the early seventies. At the time, although I didn't know it, the percentage of doctors in the US who were female was less than 10%, and the percentage who were surgeons was even smaller.

In addition, every book I read that talked about doctors, always used "he" as the pronoun, and if there was a picture it was always something like the picture shown here.

Lab coat, stethoscope, maybe a black bag, but most importantly, guaranteed, it was a picture of a male doctor. True, there were female doctors, and female surgeons, when I was a child, but nobody ever pictured doctors as being female. Thus, the riddle was a bit tricky. Your brain automatically pictures a surgeon as male, because that's how you've been conditioned over time to picture surgeons!

In the US, where I live, things have changed a lot since the days when I was a kid. Now the percentage of surgeons who are female is significantly higher. Of course, it depends on the field of surgery; OB/GYN surgeons are almost 50% female. Other areas have a much smaller percentage of women in them. Pediatric surgery is just a little under 20% female.

So we don't tend to automatically assume that a surgeon is male, and the riddle seems less perplexing.

The percentage of women in surgical fields varies depending on where you live. In your part of the world, although there is a very high rate of females who attend medical school (I think I read that in one of the neighboring countries to yours, more than 50% of students enrolled in medical schools in 2015 were female), a very small percentages of them go into surgery. I'm not sure why that is; it would be an interesting sociological question to explore! Regardless, since the percentage of female surgeons is much smaller, the riddle didn't seem quite so obvious to you.

Someday, probably, this riddle will stop being told altogether, and children will learn the riddle by reading sites like this one, and they'll say, "What? People didn't know that women can be doctors?"

Hi, there's a video going around in which a guy (Rick Lax) asks you to pick a state, and then he guesses what it is. I don't know how he does it. Kara

Well Kara, first of all, he doesn't do it. At no point in the video does he guess your state. He's a magician, and his goal is to do some misdirection, and if he fooled you into thinking he did guess your state, then he succeeded in his misdirection. Let me talk you though what he did, and then I'll talk you through how he did it (and by the way, don't expect that we're going to make a habit of doing "spoil the magician's trick" posts - this is a unique case).

First, he tells you to pick a state.

Next, he subtly steers you away from two states by using them as examples. If you picked Utah or New York as your state, when he started using those two as examples, you probably said, "Oh, I better pick something different." Ironically, if you'd stayed with your original pick, he would have gotten it wrong.

Next he tells you to take note of your state name, and the last letter in the name. Here's where he uses the examples of Utah and New York, with one being "H" and the other being "K." At this point he instructs you to "lock in" your guess by clicking "Like."

And this, right here, is the one thing about Rick Lax videos that I detest. This is painfully blatant like-baiting. All of his videos seem to have some degree of like-baiting, but this one is just obnoxious. Rick, if you ever read this post, please stop doing stuff like this. Your videos are fun, and people will share them without you doing like-baiting. 

After you've rebelled against being told to "like" the video, and sat there sullenly waiting for him to continue, eventually he puts a bunch of letters on the screen (as shown above) and asks you to find your letter. After he gives you a few seconds, he tells you that your letter is RED.

Wow! How did he do it? Well, unless you picked Wyoming (the G is blue) or Utah or New York, every other state name in the United States ends in A, D, E, I, N, O, S,T, or Y.

All of which are red. In other words, there are only three states you can pick which don't end with a red letter.

Why didn't he just make the H, K, and G red? Maybe because that would be too much red (as it is, he stuffed the whites and blues by including the letter H three times). Maybe because he figured that getting it right 47 out of 50 times is more impressive than being right all the time. After all, if he's right 100% of the time, people might try harder to figure out the trick, but if he's not 100% correct, people will think he's just an amazing guesser.

I don't normally "spoil" magicians' tricks on my blog, but the like-baiting means that this video will keep showing up on people's news feeds not because it's so good, but because they get "pushed" into liking it. Really, Rick. Seriously. The like-baiting and share-baiting makes you look pathetic, and you're really not - you're better than that! One of the best comments I saw on your video was: "You'd make a great used-car salesman." Really. That's not how you want to be seen!

So, if you like his videos, then "like" them. Don't "like" them because he told you that you have to!

Professor Puzzler

P.S. - He's got some videos that have some fun number theory in them, and I'd like to do posts on them, just because I love number theory, but I hate spoiling the fun!

Annabelle from England asks, "A farmer had 30 cows and 28 chickens.how many are left?"

Well, Annabelle, I think you may be conflating two different riddles that are somewhat similar, because I've never heard that riddle stated like that. 

Here are the two riddles I have heard, which are similar:

Riddle One: A farmer has 26 sheep and 2 died. How many are left?

Riddle Two: A farmer has 30 cows and 28 chickens. How many didn't?

The problem is that neither of these riddles are fair if you put them in writing, because they rely on similarities of spoken words to trick the listener. Once you commit it to writing, it's no longer a fair question.

You see, in riddle number one, if I was asking it out loud, what I would really be saying is: "A farmer had twenty sick sheep, and two died." So clearly the answer is 18, instead of the 24 you were expecting.

In the second riddle (which sounds like it makes no logical sense), the question (when spoken) is actually "A farmer has 30 cows, and 20 ate chickens." So if there were 30, and 20 of them ate chickens, 10 didn't.

So there you go.  A couple riddles that aren't fair to commit to writing, but are fun if you speak them aloud!

And while we're on riddles, here's a riddle I told some people at my school, and then told them, "In five minutes you won't be able to tell this riddle to anyone."

The riddle is: "Do you know how long cows should be milked?"

And the answer is: "The same as short ones."

Five minutes later I asked them to repeat the riddle back to me, and I got things like:

"How long should you milk a cow?"
"How do you milk a long cow?"
"How are long cows milked?"

It's a fun riddle, because if you don't word it exactly the way I did originally, it spoils the joke!