Interesting logic problems

144

 

9 + 7 = 144

Here is mine;

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

Then
9 * 10 = ????

eta; Too bad I put my own and was too late to be the first answer... *sigh*

It is daytime?

 

Well you never said it was night time, but you did say "there is no illumination from anywhere". Sunlight even on a cloudy day would be "illumination". Since vision requires illumination, and there is "no illumination", you did not "see" the dog.

 

This rules out daylight, lightning, flashlights or self-illumination, such as Superman's X-Rays, if you were Superman. Ergo, you never saw the dog. It was Chuck Norris's dog, and Chuck Norris doesn't need illumination to see. He stepped out and stopped your car just in time with a karate kick.

 

Maybe Tony's car has a proximity detector and it stopped itself. Does infra-red count as 'illumination'?

Or maybe it was a vampire dog with glowing eyes.

But never mind the dog - how did he drive down the street without seeing where he was going?

 

Two mathemeticians were in a bar celebrating the publication of their joint paper "Practical Applications Involving Utilization of Large Values of 1 for Tax, Bank and Other Non-Comformative Accounting". As they sipped their drinks one of them idly maneuvered some loose toothpicks around on the bar top.
"Look at that!" he suddenly exclaimed. "With just four toothpicks I've represented a number more than 5 times bigger than the world's wealthiest man's net worth!"
"Tsk," his partner scoffed, finishing her olive. "That's nothing. Here." She reached over and rearranged one toothpick, took the olive pit out of her mouth and placed it in the new arrangement. "There," she said, "is a number larger than the number of electrons in the known universe!"

What were the two arrangements of the four toothpicks (and olive pit in the second arrangement)? The toothpicks were whole, neither broken nor deformed.

 

In Tony's problem, the only answer I can think of is that his car was equipped with sonar, and it signals the driver using sound. Otherwise, daylight, lightning, luminescent eyes, are all forms of illumination.

(But I suspect that Tony was thinking "artificial illumination" and wanted "daytime" as the answer.)

In the case of the toothpicks, I can only think that the guy wrote what amounted to 11 to the 11th power. The gal could have used the olive pit as a zero and made 11 to the 110th power, but that would not have involved moving a toothpick.

 

I may have to accept that as an answer, although relative to the length of a toothpick an olive pit's size is closer to something other than a zero (think punctuation), and thus does require shifting a toothpick to make sense. 11 to the 110th is a bigger number than the number of electrons counted so far in the universe (not one by one, at least not by anyone we know), but the puzzle answer is a number that makes 11 to the 110th power petty cash by comparison. What's a quantity the number of electrons in the universe would only be about the square root of? That's the magnitude of the answer.

 

I tried to figure out how to express a google or a googleplex with four toothpicks or four toothpicks and an olive pit. I suppose the pit could be a decimal point.

A very cursory google search comes up with 10^79 as the number of electrons; so the square of that would be 10^158. Getting there with four whole toothpicks and an olive pit has me baffled. I'm generally not good at these puzzles.

 

Four toothpicks and an olive?

How about "1/0=", giving an answer of 'infinity'. That should be large enough.

 

No good. 1/0 does not equal infinity. It is undefined. IOW meaningless. When you divide 100 by 10 you are making it into ten different parts, each of which is ten. You cannot divide anything into zero parts.

 

This may give it away but the olive pit standing in for a bit of "punctuation" is not doing duty either as a decimal point or the shorthand "dot" multiplication operand.

 

Oh! It's 111! (111 factorial = about 1.76 X 10^180)

 

Actually, using 10^79 as the number of electrons, that would be the square root of 10^158. That's nowhere near the magnitude of 10^180. You'd need 10,000,000,000,000,000,000,000 10^158s to make 10^180.

 

Obviously, our universe is too small. Bingo, Daniel!

So, what is there 10^180 of? Our friend Mr. Siege Engine would say it's not quite as many questions as I keep pestering him with about his revered book, and he'd be about right, but I can't use that in the puzzle. There must be 10^180 of something though.

Anyway, your turn, sir. Let's have the next puzzle.

 

Must there be? The physical universe is limited, though it is very large. Mathematics has no limits. You can always devise a number or mathematical concept that is larger than anyone else's just by multiplying theirs by 1.01. One might suggest that the number of possible permutations of all the particles in the universe arranged in a line is greater than 10^180, but that's not a "something," it's just another mathematical concept. I don't think there's 10^180 of anything real. Of course, 10^180 is as near zero as makes no difference if you compare it to a googolplex. And that's nothing compared to a googolplexplex (10 raised to the power of a googolplex), and I could invent a number: googolmetaplex, defined as 10 raised to the googolplex power, and that raised to the googolplex power, etc., until you have raised the result to the googolplex power a googolplex number of times. And you could top that without even raising a sweat.

I cannot think of a logic problem. I'm not normally into logic problems. So rather than kill the thread I'll open it up to anyone who has a good one.