$30DNF - Math Riddle - April is Math Awareness Month!

[Nexus]

Not much left of April, but let's give this a go! I'll ask 3 riddles, and add a new one after the previous is solved.

$30DNF to each winner, $1DNF for everyday of this month!
----------------------------
RIDDLE #1 of 3

How quickly can someone
solve the following equation?

A+B= 4
B+C=10
A+C=8
A+B+C=?

TIGGA GOT IT!
----------------------------
RIDDLE #2 of 3

Three people walk into a hotel. They are told that their room will cost $30. Each man pays $10 before going to the room. The attendant realizes too late that their room only costs $25! A hotel assistant is dispatched to the room with $5. Each man gets $1 back, and the hotel assistant is given a $2 tip.

There's a problem, while they ended up paying $9 each for their room something doesn't seem to add up. Considering the hotel assistant's $2 tip, that's only $29 total. Where's the missing dollar?

----------------------------
RIDDLE #3 of 3

Look at this equation:
473+589 = 1062

Notice that all digits from 0 to 9 are used to create two summands and a sum.

How many DISTINCT solutions are there total, given the same rules? "Distinct" meaning you're not allowed to switch the order of the two summands and call them a new solution. In the example above, "473+589 = 1062" and "589+473 = 1062" should not be considering a "distinct" solution (the commutative property of addition doesn't work for you here!)

$90DNF to the last winner.
----------------------------

~ Nexus

 

[tigga]

11

 

[Nexus]

Too easy! Riddle #2 has been added.

~ Nexus

 

[GeorgeK]

There's no 'missing' dollar.

The men paid 3x$9 or $27.

$25 went to the hotel.
$2 went to the tip.

$25+$2 = $27

 

[Spider]

Room was $25, each man was given $1 each and remaining $2 was given as a tip. I don't really see anything wrong, $25+$3+$2=$30. They didn't pay $9 each, they paid $8.33 each.

 

[tigga]

They pay $9 each and the $2 is deducted to equal $25, not added to equal $29 - what GeorgeK said.

 

[Nexus]

GeorgeK gets it! (Still too easy, I have to work on these!)
Riddle #3 has been added.

~ Nexus

 

[DomeBase]

OK: here goes... folks want something more challenging...

The Poisson process is often taken to be a good starting place for modeling spike trains. Spike trains from functionally related neurons are often positively or negatively correlated at short lags. Is it possible to construct a pair of point processes, each of which is Poisson when viewed in isolation, whose cross-correlation is negative at short lags? I'll give you a hint. This may have something to do with Canoe.biz!

 

[tigga]

Originally posted by DomeBase
OK: here goes... folks want something more challenging...

The Poisson process is often taken to be a good starting place for modeling spike trains. Spike trains from functionally related neurons are often positively or negatively correlated at short lags. Is it possible to construct a pair of point processes, each of which is Poisson when viewed in isolation, whose cross-correlation is negative at short lags? I'll give you a hint. This may have something to do with Canoe.biz!

Ummmmm...... Yes, it is possible.

 

[Nexus]

Originally posted by DomeBase
OK: here goes... folks want something more challenging...

Newsflash: In recent news, the dotInfo Internet namespace evangelist often referred to as "DomeBase" on popular web forums, has had a class action lawsuit filed against him for "breaking people's heads". When questioned, many of those joining in the suit could only scratch their heads and point at the offending posts and say "he baaad man". While rehabilition will undoutably help these wretched souls, many of us will continue to ask why these Internet fiends are free to engage in these mindless acts of cerebral sabotage.

~ Nexus :razz:

 

[Nexus]

SOME CLUES:
1.) They will have this format:
XXX + XXX = XXXX
2.) All of the sums will be unique.
3.) Items like "069" or "0134" do not legally represent the "0" as part of the equation so they don't count. They end up being 69 and 134 respectively.
4.) All of the sums will be >999 and <2000

~ Nexus

 

[stevo]

Riddle #3---- All numbers between 0 and 9 are represented in the equation.

Edit--- Hey, Did I miss something?

Edit II--- All I saw was the question, not the riddle.

 

[Nexus]

Originally posted by stevo
Riddle #3---- All numbers between 0 and 9 are represented in the equation.
Edit--- Hey, Did I miss something?

I just tweaked the clue to read more clearly. Specifically, "069" doesn't work, but "609" works. "0198" doesn't work, but "1980" works fine.

Originally posted by stevo
Riddle #3---- All numbers between 0 and 9 are represented in the equation.
All I saw was the question, not the riddle.

I'll update that to be clearer, the problem was a little further down.

Originally posted by Nexus
How many DISTINCT solutions are there total, given the same rules? "Distinct" meaning you're not allowed to switch the order of the two summands and call them a new solution. In the example above, "473+589 = 1062" and "589+473 = 1062" should not be considering a "distinct" solution (the commutative property of addition doesn't work for you here!)
$90DNF to the last winner.

~ Nexus

 

[DomeBase]

Originally posted by Nexus
Newsflash: In recent news, the dotInfo Internet namespace evangelist often referred to as "DomeBase" on popular web forums, has had a class action lawsuit filed against him for "breaking people's heads". When questioned, many of those joining in the suit could only scratch their heads and point at the offending posts and say "he baaad man". While rehabilition will undoutably help these wretched souls, many of us will continue to ask why these Internet fiends are free to engage in these mindless acts of cerebral sabotage.

~ Nexus :razz:

Your Brain Is Fine
Gonna Take You Right
Just Show Your Answer
In the Broad Daylight
I'm Telling You
You Got Wonk Appeal
Won't Hurt Your Mind
If the Neurons Feel
Come On, Come On,
Let it Come Out Right...

Because I'm Bad, I'm Bad-
Come On
(Bad Bad-Really, Really Bad)
You Know I'm Bad, I'm Bad-
You Know It
(Bad Bad-Really, Really Bad)
You Know I'm Bad, I'm Bad-
Come On, You Know
(Bad Bad-Really, Really Bad)
And The Whole World Has To
Answer Right Now
Just To Tell You Once Again,
Who's Bad . . .

:evil: :swg:

 

[WildCard]

hmm, if there's a mathmatical solution to #3, I would love to see it. I think the most practical way to do it (for a dummy like me), would be to program something in VB to start from the bottom and work the way up, keeping track of the situations where the equation is true.

Nice twist to make it so that 0 can't be in number place 1, 4, and 7.

Bet someone could do this pretty easily.

-WC-

 

[Nexus]

Originally posted by WildCard
hmm, if there's a mathmatical solution to #3, I would love to see it. I think the most practical way to do it (for a dummy like me), would be to program something in VB to start from the bottom and work the way up, keeping track of the situations where the equation is true. Nice twist to make it so that 0 can't be in number place 1, 4, and 7. Bet someone could do this pretty easily. -WC-

I'll admit I used PHP locally to run a manual check on the permutations. A programming "test" for myself this morning.

~ Nexus

 

[llew]

48 DISTINCT solutions.

Originally posted by Nexus

----------------------------
RIDDLE #3 of 3

Look at this equation:
473+589 = 1062

Notice that all digits from 0 to 9 are used to create two summands and a sum.

How many DISTINCT solutions are there total, given the same rules? "Distinct" meaning you're not allowed to switch the order of the two summands and call them a new solution. In the example above, "473+589 = 1062" and "589+473 = 1062" should not be considering a "distinct" solution (the commutative property of addition doesn't work for you here!)

$90DNF to the last winner.
----------------------------

~ Nexus [/B]

 

[WildCard]

I say you have to explain how you got your answer when you make a guess! Show us how you did it!

-WC-

 

[peter]

I could easily solve it with permutations in c++ or php (the only languages I know), but that would be cheating.

However, I don't think there is a way to solve this without that

 

[llew]

You'll have to ask Gérard P. Michon, Ph.D. for the steps, he solved it on 10/10/2000.

The answer, which I worked out after posting the question, is 48. Listed below are the basic 6 pairs of solutions. Each of these represents 4 distinct solutions obtained by switching digits between the two summands. (We count as distinct only different pairs of summands, not the same pair in a different order.)

879+426 = 1305 & 879+624 = 1503
859+347 = 1206 & 859+743 = 1602
789+264 = 1053 & 789+246 = 1035
756+342 = 1098 & 765+324 = 1089
657+432 = 1089 & 675+423 = 1098
589+473 = 1062 & 589+437 = 1026