Sven's Official BrainTeaser Thread !! and Sander.

[sputnik]

all i can figure out is that the perfectsquare is an odd number. lol

i cant think of 'an easy' way to figure this out

[Mike]

I think I solved it, but my way is far from quick or easy.

for the uncool solution:

Let  p1 and p2 be the two primes and s be the perfect square.

p1 + p2 + s = 2009.

since both p1 and p2 are odd, s must be odd aswell.

so s has a range from 10^2<s<32^2 (cannot be higher than 1000)

or to be more precise: s = 11^2 (121), 13^2(169), 15^2(225), 17^2(289), 19^2(361), 21^2(441), 23^2(529), 25^2(625), 27^2(729), 29^2(841) or 31^2(961)

but since the digits cannot be the same:

s = 13^2(169), 17^2(289), 19^2(361), 23^2(529), 25^2(625), 27^2(729), 29^2(841) or 31^2(961)

The only way I can see how to find the numbers with a bit of ease, is to set s really low and then force the primes to be high and therefore I don't have to search through many primes, seeing as there are less primes the higher you get.

the lowest perfect square with the conditions is 169, so set s = 169 and put it in the equation

p1 + p2 + 169 = 2009
p1 + p2 = 1840

let p1>p2

then p1>1840/2(920)

The closest prime to 920 with the conditions is 937, but if p1=937 then p2 is no prime.

we can see

920<p1<1000

and then:

800<p2<900

so substitute p1 = q1 + 900 and p2 = q2 + 800

then

q1 + 900 + q2 + 800 = 1840
q1+q2 = 140

try for q1>q2

then q1 > 140/2(=70)

and the only two primes with a q1 being more than 70 is 971 and 983.

Luckily, 1980 - 983 = 857, which also is a prime.

the primes are: 857, 983
the perfect square is: 169

But I think I know another way. I'ma see if it's easier and then post it later.

[VG]

Unfortunatley that isn't the right answer, and you have done it the hard way don't forget there are no repeated numbers in any of the 3 figure numbers, this means yours is wrong mike cos in 857,983 and 169 the 9 and the 8 are repeated in 2 numbers  :thumbsup:.  Sputnik your on the right lines with the perfect square don't give up

Just a small addition unique numbers means numbers 0-9 including 0

One more bit of advice when your working it out if you set the numbers out like this:

   xxx
   xxx
   xxx
   ----    +
   2009

Then you may find a pattern that can help you

[Mike]

ooh, that makes it much easier. I didn't know they wern't allowed to repeat in the different numbers.

Well then

prime 1 = 100a1+10b1+c1
prime 2 = 100a2+10b2+c2
square = 100a3+10b3+c3

the 9 in 2009 depends on c1+c2+c3, so the sum of those is either 9 or 19. Let's try for 9.

c1,c2,c3 are all odd, and 9 can only be 1+3+5 then.
5 is never a prime, since it devisable with 5. So it's the square, and the only square is 25^2=625.
so b1+b2+b3 is either 10 or 20, 10 = 2+8+0
then a1+a2+a3=18, with a3 = 6. a2+a3=13 with the only unrecurring solution 9+4.

putting together you get:

The square is 625
prime 1 = 983
prime 2 = 401

c1+c2+c3 = 19 you won't be able to solve it. You can try.

This one's correct?

[Sander]

mike you are an awesome googler or very smart. i think the it's the last one ;)

[VG]

Yes mike you are right :thumbsup:

[Mike]

I am no googler :cursing: . But thank you :cheers:

A bathtub gets filled using the warm water pipe in 8 minutes. Using the cold water pipe it takes 6 minutes. The sewer drains the water in 4 minutes. If every pipe is open, (including the sewer), will the bathtub ever get filled? If so, when?

[Sander]

I am no googler :cursing: . But thank you :cheers:

A bathtub gets filled using the warm water pipe in 8 minutes. Using the cold water pipe it takes 6 minutes. The sewer drains the water in 4 minutes. If every pipe is open, (including the sewer), will the bathtub ever get filled? If so, when?

it can't be filled.
the sewer takes away water in 4 min what the water pipes must bring in (6+8)/2=7 minutes. the bath can only be filled if the water can be brought by the water pipes in under 4 minutes. if you think that having all water pipes open makes the water get this speed, then it's possible, but according to my calculations it's 7 min, so it can't

[VG]

yes it will in minutes i get it to around 22 minutes if you want my more exact answer of seconds i got around 1315 seconds.  Will post working later as i have to run to get to my hockey match.

Easy way to see that the bath does fill take the % of the bath filled per second for both taps is 0.486% and % of bath drain per second by sewer which is 0.41% therfore always 0.076% of the water left i think per second do 100/0.076 and you get 1315 seconds

[Mike]

I am no googler :cursing: . But thank you :cheers:

A bathtub gets filled using the warm water pipe in 8 minutes. Using the cold water pipe it takes 6 minutes. The sewer drains the water in 4 minutes. If every pipe is open, (including the sewer), will the bathtub ever get filled? If so, when?

it can't be filled.
the sewer takes away water in 4 min what the water pipes must bring in (6+8)/2=7 minutes. the bath can only be filled if the water can be brought by the water pipes in under 4 minutes. if you think that having all water pipes open makes the water get this speed, then it's possible, but according to my calculations it's 7 min, so it can't

So if the bathtub is filled with both cold water and warm water it takes longer time than with only cold water? The cold water pipe and the warm water pipe don't share a pipe, they are two separate.

VG; 22 minutes is incorrect, but it's really close. Maybe you've done some wrong in you calculus, but I can't point it out as I'm not 100% sure of what you've done.

[VG]

Ok so what i've done is  first converted it all into seconds so you have 8*60 and 6*60 so this gives you 480 and 360 this is the time for the bath to become 100% full for either tap on its own so calculate the % the bath fills up for 1 second for both tap and you get 0.2083% and 0.2777% respectively if you add these 2 figures together you get 0.486% of the bath fills up per second.

The plug takes away all the bathwater in 4 minutes  seconds and we can say that so if we convert that into seconds we have 240,  now we work out how much water is drained per second in % and we get 0.4166.

If we then do 0.486 - 0.4166 we get 0.0694.  This is the % that the bath is filling up every seond so to find out how long it takes we do 100/0.0694 and we get 1440.922 seconds divide this by 60 and we have 24.01 minutes so i think my calculating was off first time.

[sputnik]

23.998 (24 minutes) i believe is correct, but when rounded its the same as VG

100/[((100/8)+(100/6))-(100/4)]= 23.99999998 to however many dp