Interesting logic problems

Hey airportkid, what was the first number posted? I had 11^11 for the first one and 111! for the second.

 

If
5 * 6 = 570
6 * 7 = 1218
7 * 8 = 2296
8 * 9 = 3960

Then
9 * 10 = ??6390??

I need help with this one!

How did you get 6390?

 

Thyme (time) heals all wounds.

 

Here's one I just made up.

The following is an addition (normal base ten addition with no tricks ok). Each letter in the sum represents a unique digit 0 though to 9. The object is to find an assignment of letters to digits that makes the sum add up correctly.

Code:

    J I M
            +
S I K E S
---------
C H E A T

That is, JIM + SIKES = CHEAT.

 

Actually, there is a very very easy way to get the hidden numbers. Just subtract the sum of the two numbers from the answer.

So for 5 * 6, you subtract 5 + 6 (11) from the answer of 30 to get 19.

((A * B) - (A + B)) * (A * B) = C
((5 * 6) - (5 + 6)) * (5 * 6) = 570
(30 - 11) * 30 = 570
19 * 30 = 570

I`m glad that someone was stumped by something I though up in a minute or so. And fascinating to see this different way used to solve it.

 

Interesting, I did it yet another different way. I calculated the "hidden number" simply as (A-2)B + 1.

For example for the last product, A=9 and B=10. The missing factor is :
(9-2)*10 + 1 = 7*10 + 1 = 71.

BTW Has anyone tried my JIM SIKES puzzle yet. It's a real puzzle and not just a joke, it has an actual solution in case anyone was wondering.

 

Me too. That's why I just pass over them without a second thought.

There is no such thing as "very unique." The word unique means one of a kind. There is no such thing as "very one of a kind." Something can be very unusual, but not very unique.

Your number appears to have all ten digits, each one only once. Beyond that, I'll let someone else figure out why it's unique.

Of course, I could say that 1084319]8549176320 is unique because it occurs only once in the list of all integers. But I hope you have something more interesting to say about it than that.

 

I was going to say garlic. Which of course is ail in French, and must be good for ailments.

 

Nice one Eagle.

Actually there was (at least) one other solution. I did try to make one with a unique solution but it was too hard.

Another solution is.
JIM + SIKES = CHEAT
793 + 19861 = 20654

Hi Daniel. It's not all random guessing with this type of problem. You can often deduce a few of the assignments to get a starting point. For example in this case it's pretty easy to deduce that I=9 and H=0 and that C = S + 1. After that it is quite a lot of guess work though.

 

Hi eagle, I've seen this one before (and it did totally stump me then). It's very tricky because most people will approach it purely as a numerical problem while it's actually a word problem in disguise.

It's the digits 0 through 9 arranged in alphabetic order.

 

Ok trying to keep it topical, heres another original I just made.

Dave, Fred, Jim and Kate have all calculated the lifetime average MPG of their cars to the nearest whole number (of mpg's). Comparing their results they find the following.

Fred's Prius gets 5 MPG more than Jim's Prius.
Jim's Prius gets twice as many MPG's as Dave's Chevy.
Kate’s Prius with plugin conversions get as many MPG as Fred and Jim put together.
The lowest of the group gets better than 22 MPG and the highest of the group gets less than 100 MPG.

How many MPG does each person get?

 

Dave is worst at 23 MPG
Jim gets twice Dave's MPG at 46 MPG
Fred gets 5 MPG better than Jim at 51 MPG
Kate gets Fred & Jim's combined MPG of 97

 

The famous Monty Hall problem had mathematics PhDs writing nasty letters to Marilyn vos Savant, but she had it right. Here it is:

You're a contestant on Monty Hall's set, and he shows you three doors. Behind two of the doors are a used pair of shoes and a box of paperclips, respectively. Behind the last door is $25,000 in cash and a voucher good for 5 years of mortgage payments. Crossing your fingers, you choose a door.

Monty does not open that door, he opens another door, revealing the used shoes.

"Would you like to change your mind," he asks, "and pick another door?"

What's your best next action? Keep the door you picked, or choose another? Specifically, what are your odds of winning the treasure if you stay with your first pick, and what are the odds of winning the treasure if you change your mind?

 

You should choose the last door. Didn't you say that's where the money is?

I'm probably not looking at this correctly, because it seems too easy. I'd say at first read through that the odds are 50%. We already know one door has the shoes, which leaves one door with the paperclips and one door with the treasure.

 

Wait. Monty KNOWS where the prize is, doesn't he? And, he opens the wrong door on purpose. Yes, change doors, because the odds are now 2 in 3 instead of 1 in 3. Man, that's tricky.

Edit: Does he know, or not? That changes it. Oh man, now I'm going to have nightmares of Price is Right all night. Do you know any word puzzles featuring Vanna White? :brick:

 

That's what all those irritated PhDs insisted. But they were wrong. 50-50 is incorrect.

 

Now you got it. That's right. Monty has to know - he's the host.

There's another way to arrive at the same answer, namely, change your mind, not mathematically but by recognizing the objective of game shows, which is to show happy people winning sponsors' prizes, not losing. Had you picked the correct door the first time, Monty would just open it, he wouldn't risk putting you in a position to lose. But two thirds of the time the wrong door will be picked the first time, and giving the contestant that extra chance improves the odds of producing a winner.