@Rohan Rao
–
They didn't even bother to change the number of people it's been solved by..I don't like remembering problems I like solving them..Please brilliant,If you are going to recycle problems,At least change the numbers
–
Thaddeus Abiy
·
3 years, 6 months ago

Log in to reply

@Thaddeus Abiy
–
I think they must have been working on the new problem bank this week and thus didn't have time to create/present new problems.
–
David Altizio
·
3 years, 6 months ago

They are probably behind, or saving something because of the revamp of curriculum mathematics that is being done. So I bet they are working very hard this week!
Lets find problems other places. If you have any good problems you would like to share, please post them as a reply so that everyone can have problems to do while waiting.

Here,
An auditorium has a rectangular array of chairs. There are exactly 14 boys seated
in each row and exactly 10 girls seated in each column. If exactly 3 chairs are
empty, find the maximum number of chairs in the auditorium.
–
Brock West
·
3 years, 6 months ago

Log in to reply

@Brock West
–
If you wanna keep this going, then here's a GREAT problem from the 1983 ARML competition:

In an isosceles triangle, the altitudes intersect on the inscribed circle. Compute the cosine of the vertex angle.
–
David Altizio
·
3 years, 6 months ago

Log in to reply

@David Altizio
–
Should I post a solution for this one? Its a fairly simple exercise in trigonometry, but there will be people still trying to solve this one.

I arrived at the answer 1/9 (assuming you are taking the cosine of the 'unique' angle)
–
Gabriel Wong
·
3 years, 6 months ago

Log in to reply

@Gabriel Wong
–
It says 'vertex angle', so yea your answer is correct.

Don't post the solution though; while its a relatively simple problem I still like it for having such an interesting condition.
–
David Altizio
·
3 years, 6 months ago

@Brock West
–
Under the assumption that boys and girls cannot share a chair, let number of rows and columns be r and c. (r >= 14; c >= 10)

Then rc = 3+14r+10c

rc-14r-10c-3 = 0

rc - 14r - 10c +140 - 143 = 0

(r-10)(c-14) = 143

Now, the possibilities for (r,c) are (1,143), (11,13), (13,11) and (143,1). Checking all 4, the number of chairs in each is (11)(157), (21)(27), (23,25), (153,15).

Clearly (23)(25) > (21)(27) and (11)(157)<(153)(15). (if a>c>d>b>0 and a+b = c+d, ab < cd)
Also, (153)(15) > (23)(25) obviously.

The maximum number of chairs is thus (153)(15) = 2295 (with 2292 chairs filled up)
–
Gabriel Wong
·
3 years, 6 months ago

Log in to reply

@Gabriel Wong
–
why ? defining X = r-10, Y = c-14, then that means
X = 1,Y = 143 -> r = 11, c 157 -> rc = 1727
X = 11, Y = 13 -> r = 21, c = 27 -> rc = 567
X = 13, Y = 11 -> r = 23, c = 25 -> rc = 575
X = 143, Y = 1 -> r = 153, Y = 15 -> rc = 2295 (This is the max number of chairs)
–
Raymond Christopher Sitorus
·
3 years, 6 months ago

Log in to reply

@Raymond Christopher Sitorus
–
I think the answer would be rc and not rc-3 though, since the three chairs that are empty are still chairs in the array.
–
David Altizio
·
3 years, 6 months ago

I hate it.. I hope they can fix it as soon as possible..
–
Neil Tinaytina
·
3 years, 6 months ago

Log in to reply

There will be a lot to look forward to; new challenges and a huge database will be up tomorrow or Tuesday. Peter T. posted this earlier. I can't find a link at the moment, sorry!
–
Ahaan Rungta
·
3 years, 6 months ago

Log in to reply

I got the same problem... Hope they fixed it soon.
–
André Macedo
·
3 years, 6 months ago

Log in to reply

problems are back yepiii!!!!!!!!!!!!!!!!!!!!!
–
Tejas Kasetty
·
3 years, 6 months ago

## Comments

Sort by:

TopNewestOh man..I even woke up early to do the new problems today.. – Thaddeus Abiy · 3 years, 6 months ago

Log in to reply

– Ahmed Abid Abbash · 3 years, 6 months ago

same over here.. sad. :(Log in to reply

Hi everyone,

This was a glitch and has been corrected. You can see new Olympiad problems now. We are very sorry for the mistake.

Happy problem solving! – Silas Hundt Staff · 3 years, 6 months ago

Log in to reply

– Thaddeus Abiy · 3 years, 6 months ago

why are some of them recycled though??Ive seen them before..or is it just meLog in to reply

– Rohan Rao · 3 years, 6 months ago

Yes, i too saw at least 2 repeated questions.Log in to reply

– Thaddeus Abiy · 3 years, 6 months ago

They didn't even bother to change the number of people it's been solved by..I don't like remembering problems I like solving them..Please brilliant,If you are going to recycle problems,At least change the numbersLog in to reply

– David Altizio · 3 years, 6 months ago

I think they must have been working on the new problem bank this week and thus didn't have time to create/present new problems.Log in to reply

– Tan Li Xuan · 3 years, 6 months ago

Yeah...Log in to reply

They are probably behind, or saving something because of the revamp of curriculum mathematics that is being done. So I bet they are working very hard this week! Lets find problems other places. If you have any good problems you would like to share, please post them as a reply so that everyone can have problems to do while waiting.

Here, An auditorium has a rectangular array of chairs. There are exactly 14 boys seated in each row and exactly 10 girls seated in each column. If exactly 3 chairs are empty, find the maximum number of chairs in the auditorium. – Brock West · 3 years, 6 months ago

Log in to reply

In an isosceles triangle, the altitudes intersect on the inscribed circle. Compute the cosine of the vertex angle. – David Altizio · 3 years, 6 months ago

Log in to reply

I arrived at the answer 1/9 (assuming you are taking the cosine of the 'unique' angle) – Gabriel Wong · 3 years, 6 months ago

Log in to reply

Don't post the solution though; while its a relatively simple problem I still like it for having such an interesting condition. – David Altizio · 3 years, 6 months ago

Log in to reply

– Ahaan Rungta · 3 years, 6 months ago

Thanks for posting! :)Log in to reply

– Jon-jon Castro · 3 years, 6 months ago

try this: 1=6 2=12 3=18 4=24 5=30 6=??Log in to reply

– Tan Li Xuan · 3 years, 6 months ago

1,because 1=6,so 6=1 :)Log in to reply

– Zi Song Yeoh · 3 years, 6 months ago

6 = 6, obviouslyLog in to reply

– Thaddeus Abiy · 3 years, 6 months ago

Yes 6=6 obviously but if the equal to mean's multiply by 6 its 36Log in to reply

– Jon-jon Castro · 3 years, 6 months ago

1 is correctLog in to reply

– Zi Song Yeoh · 3 years, 6 months ago

1 = 6 is illogicalLog in to reply

– Tan Li Xuan · 3 years, 6 months ago

because 1=6,so 6=1Log in to reply

Then rc = 3+14r+10c

rc-14r-10c-3 = 0

rc - 14r - 10c +140 - 143 = 0

(r-10)(c-14) = 143

Now, the possibilities for (r,c) are (1,143), (11,13), (13,11) and (143,1). Checking all 4, the number of chairs in each is (11)(157), (21)(27), (23,25), (153,15).

Clearly (23)(25) > (21)(27) and (11)(157)<(153)(15). (if a>c>d>b>0 and a+b = c+d, ab < cd) Also, (153)(15) > (23)(25) obviously.

The maximum number of chairs is thus (153)(15) = 2295 (with 2292 chairs filled up) – Gabriel Wong · 3 years, 6 months ago

Log in to reply

– Raymond Christopher Sitorus · 3 years, 6 months ago

why ? defining X = r-10, Y = c-14, then that means X = 1,Y = 143 -> r = 11, c 157 -> rc = 1727 X = 11, Y = 13 -> r = 21, c = 27 -> rc = 567 X = 13, Y = 11 -> r = 23, c = 25 -> rc = 575 X = 143, Y = 1 -> r = 153, Y = 15 -> rc = 2295 (This is the max number of chairs)Log in to reply

– David Altizio · 3 years, 6 months ago

I think the answer would be rc and not rc-3 though, since the three chairs that are empty are still chairs in the array.Log in to reply

– Raymond Christopher Sitorus · 3 years, 6 months ago

thx David for correctingLog in to reply

– David Altizio · 3 years, 6 months ago

Why doesn't, say, r=21 and c=27 work?Log in to reply

– Gabriel Wong · 3 years, 6 months ago

was wrong initially, editedLog in to reply

I hate it.. I hope they can fix it as soon as possible.. – Neil Tinaytina · 3 years, 6 months ago

Log in to reply

There will be a lot to look forward to; new challenges and a huge database will be up tomorrow or Tuesday. Peter T. posted this earlier. I can't find a link at the moment, sorry! – Ahaan Rungta · 3 years, 6 months ago

Log in to reply

I got the same problem... Hope they fixed it soon. – André Macedo · 3 years, 6 months ago

Log in to reply

problems are back yepiii!!!!!!!!!!!!!!!!!!!!! – Tejas Kasetty · 3 years, 6 months ago

Log in to reply

They're up now. – Kenneth Chan · 3 years, 6 months ago

Log in to reply

Why arent there any qns today? I thought they post qns here every Monday?!?! – YuJiahuan LuvRafflesfriends · 3 years, 6 months ago

Log in to reply

I hope they will bring new things.I will wait with patience – Shaheed Vh · 3 years, 6 months ago

Log in to reply

:( – Advitiya Brijesh · 3 years, 6 months ago

Log in to reply

But atleast they could send the weekly problems of one of the Olympiad sections. I'll get bored.... – Garvil Singhal · 3 years, 6 months ago

Log in to reply

Hopefully it's just because they're upgrading the techniques trainer. – Clifford Wilmot · 3 years, 6 months ago

Log in to reply

– Vishwa Iyer · 3 years, 6 months ago

HopefullyLog in to reply

i cant see my trignometry & calculus problems since 2 weeks... – Nikhil Tr · 3 years, 6 months ago

Log in to reply

– Nikhil Tr · 3 years, 6 months ago

can you??Log in to reply