The worlds first riddle!

If it's the ## * # = ## + ## = ## problem I posted several pages back, I already answered Try's question about uniqueness.[/quote]

Actually I was referring to this problem:

"Use all the numbers 1 2 3 4 5 6 7 8 9 in that order.
Insert +, -, *, and / or parentheses between the numbers to find a total of 30"


Numbers = 30


Thoh: #s: 1(2+3)4/5*6+7+8-9

Mark: ((12-(3x4))x5)+6+7+8+9

Me: (1+2)*3+4+5+6+7+8-9=30


There may well be more.

Stormy is buying a gold ring set with stones for Try on his birthday. A ring set with 4 amethysts and 1 diamond comes to US$2,000. One with 3 emeralds, 1 amethyst and 1 diamond would be US$1,400. And one set with 2 rubies and 1 diamond would cost US$3,000. Being a thoughtful person, she chooses a ring with 4 stones, each representing one of her 4 children.

As her children are named Andy, David, Ellen, and Richard, how much in US$ will the ring containing 1 Amethyst, 1 Diamond, 1 Emerald, and 1 Ruby cost her

$2,300 and she better not tell her husband!

Any other riddles, Try?

Yugi is sitting in a car that's not moving with a helium-filled balloon, which is resting up against the car's ceiling somewhere near its middle. The driver hits the gas and the car accelerates forward, throwing her back into her seat.

What happens to the balloon

if there is helium in it it should stay in place. or at the right speed it could pop.

The driver is not thrown into his seat, the seat is thrown into the driver, which at first compresses the driver and the seat as it starts to accelerate him. Likewise the back of the car moves up and hits the balloon, although not before slight torque is applied to the balloon causing it to rotate in the direction of motion, from the friction forces at the top. Fluid dynamics of the air further complexify the motion.

The only thing that could cause the balloon to pop is if air pressure inside the car were dramatically increased. If the windows are closed air pressure will not change at all. If the windows are open then there would be a slight non-uniform increase of overall pressure due to turbulence of the air being rammed in but this would be very minimal and certainly not enough to pop the balloon.

I think a decrease in air pressure would be required to pop the balloon. An increase would decrease the size of the balloon.

haha, yes...of course excuse the dyslexic logic there.

DIGIT PROBLEM SOLUTIONS

Checking all possible postfix notation solutions (excluding digit concatenation and unary minus), I found over 58,000 solutions. Of course, many of these are equivalent due to associativity.

Associativity? But you can't change the order of the digits.

There are infinite solutions if you allow parenthesis because you can always add more parens without changing the result, so for the purposes of the question, only consider the order of the 8 operators to represent unique solutions. That is, operators chosen from the set {*,+,-,/} distributed between the 9 digits.

a) According to this definition of uniqueness, how many unique orderings are possible?

b) exactly how many of those orderings can be made a valid solution with the use of parenthesis?

Stu:

BRIDGE:

s = r*theta

on the surface:
s1 = r1*theta
4260 ft = 4000*5280*theta
theta = 4260/(4000*5280) = 2.017E-4

at the bridge level:
s2 = r2*theta
s2 = (4000*5280+690)*4260/(4000*5280) = 4260.139

Difference = s2-s1 = 4260.139 - 4260 = 0.1392 ft



The radius of the Earth is 4,000 miles (21,120,000 feet). Therefore, for every 21,120,000 feet of 'height' the bridge spans 4,260 feet. This makes a 4,957.7 to 1 'rise to run' ratio. So, for the final 690 feet of 'height', the bridge must span an additional 690/4957.7 feet or .13918 feet or 1.670 inches.




DAYS OF THE WEEK:

Stu:

1*6/7*5/7*4/7*3/7*2/7*1/7 = 0.00612



The probability that 1 person would NOT be born on the same day of the week as 1 other person is six out of seven. Continuing that reasoning, with 3 people it would be 5 out of 7 and so on. So the probability that ALL seven people would be born on a different day of the week is:
(6/7) x (5/7) x (4/7) x (3/7) x (2/7) x (1/7) which equals:
.006119899022 or1 in 163.4013889.


Stu, I am the first to admit I'm no dietation, however, may I suggest you increase your calorie intake.



Try's birthday

Stormy: $2,300


The puzzle gives the following formula:
4amethyst + diamond = 2000
3emerald + amethyst + diamond = 1400
2ruby + diamond = 3000
ring = emerald + ruby + amethyst + diamond
Rewriting the amethyst and ruby formula gets:
amethyst = 500 - diamond/4
ruby = 1500 - diamond/2
Substituting the amethyst into the emerald formula we get:
3emerald + amethyst + diamond = 1200
3emerald + 500 - diamond/4 + diamond = 1400
3emerald = 900 - 3/4diamond
emerald = 300 - diamond/4
Now substituting into the ring formula we see that the diamond drops out:
ring = amethyst + diamond + emerald + ruby
ring = (500 - diamond/4) + diamond + (300 - diamond/4) + (1500 - diamond/2)
ring = 2300 - diamond/4 + 4diamond/4 - diamond/4 - 2dimond/4
ring = 2300
This means that the ring will cost US$2300. Let's say diamonds are US$0 at this store. That would mean that amethyst = US$500, emerald = US$300, and ruby = US$1500. 300 + 500 + 1500 = 2300. That works. Let's say diamonds were US$100. That would mean that amethyst = US$475, emerald = US$275, and ruby = US$1450. 475 + 100 + 275 + 1450 = 2300. Works.



Stormy wrote, "…this doesn't mean my plastic surgery makeover is off now does it?"

Not after an answer like that. Do you want a nip and tuck, or a boob job?



Talking about inflatables: What happens to the balloon

It seems like it would go back in the car with everything else, however it will actually move forward. When the car accelerates forward, the heavier air will try to move to the back of the car and the lighter than air balloon will be pushed forward. Don't believe me, try it.





You are taking a cruise: London, England to New York City, USA. The passage takes an hour less than 7 days (167 hours) and then the ship is in port 23 hours before returning.

The cruise line has ships which depart from NYC and London every day of the week at precisely 10:00 GMT. The ships all sail along the same route so as you make the passage, you will pass by other ships from the cruise line traveling in the opposite direction.


How many of the cruise line's ships will you pass by going in the opposite direction while making this voyage

how long did that take you to write?

As long as it took me to write:



How long will an 8 day clock run without winding



Take 2 letters from a 5 letter word and have one left



What is the longest sentence in the world

trips, remove r and s and you have 1 word, tip



There isn't one, because there are infinite sentences that have infinite length.

One would be:

"I am going to say the following words: a, at, at, adjunct, ..."

You missed aardvark, so that wouldn't be the longest sentence.

You're confusing associativity with commutativity.


Agreed, but my solution doesn't add redundant parens. Admittedly, many are unnecessary.



Good idea. The problem is better defined. Can I assume that unary minus is not allowed (also leads to infinite number of solutions)?
Also, your mention of 8 operators implies digit concatenation is not allowed.



Well that's easy if you don't require the result to be 30: 4^8


Unless I've misunderstood (a), I'd add:
c) How many of the unique orderings provide a valid solution (30) without parens (standard precedence rules apply)?

[size=8]It won't run without winding.
phone - ph = one
multiple life sentences[/size]