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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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0 replies
jlacosta
Apr 2, 2025
0 replies
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Eazy equation clap
giangtruong13   1
N an hour ago by iniffur
Find all $x,y,z$ satisfy that: $$\frac{x}{y+z}=2x-1; \frac{y}{x+z}=3y-1;\frac{z}{x+y}=5z-1$$
1 reply
giangtruong13
Yesterday at 4:03 PM
iniffur
an hour ago
J
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Excalibur Identity
jjsunpu   13
N 3 hours ago by anduran
proof is below
13 replies
jjsunpu
Apr 3, 2025
anduran
3 hours ago
J
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Problem nt
HopefullyMcNats2025   1
N 4 hours ago by HopefullyMcNats2025
How many positive integers from 1-100000 fit the conditions, they are not divisble by 3, 5, or 8 and that they are palindromes,
1 reply
HopefullyMcNats2025
4 hours ago
HopefullyMcNats2025
4 hours ago
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Inequalities
nhathhuyyp5c   4
N 4 hours ago by maxamc
Prove that for all positive real numbers \( a, b, c \), the following inequality holds:

\[ \sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}} \]
4 replies
nhathhuyyp5c
Today at 4:45 AM
maxamc
4 hours ago
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No more topics!
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min shots to sink a 3ship in 7x7 battleship (2005-06 Savin Competition 6-8 p20)
parmenides51   11
N Jun 25, 2021 by tigerzhang
There is a game of "battleship". A three-deck ship is hidden on a $7 \times 7$ checkered field. In what is the smallest number of shots you can probably sink it?
11 replies
parmenides51
Jun 11, 2021
tigerzhang
Jun 25, 2021
J
min shots to sink a 3ship in 7x7 battleship (2005-06 Savin Competition 6-8 p20)
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Reveal topic tags
geometry
combinatorics
game
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parmenides51
30629 posts
parmenides51
#1 h  Jun 11, 2021, 4:41 AM • 2 Y
Y by centslordm, Mango247
There is a game of "battleship". A three-deck ship is hidden on a $7 \times 7$ checkered field. In what is the smallest number of shots you can probably sink it?
This post has been edited 2 times. Last edited by parmenides51, Jun 11, 2021, 5:11 AM
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greenturtle3141
3541 posts
greenturtle3141
#2 h  Jun 11, 2021, 6:53 AM • 2 Y
Y by russellk, centslordm
Solution that actually doesn't work oh well
This post has been edited 1 time. Last edited by greenturtle3141, Jun 16, 2021, 7:02 PM
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biscuit02
636 posts
biscuit02
#3 h  Jun 11, 2021, 9:13 AM • 3 Y
Y by BakedPotato66, centslordm, Mango247
greenturtle3141 wrote:
Solution

Click to reveal hidden text
This post has been edited 1 time. Last edited by biscuit02, Jun 11, 2021, 9:17 AM
Reason: typo
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greenturtle3141
3541 posts
greenturtle3141
#4 h  Jun 11, 2021, 5:13 PM • 1 Y
Y by centslordm
In that case, even if you do find the ship, you'll need at least 5 more shots to sink it. Either way this makes the problem much more complicated and the solution is no longer necessarily optimal.
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juliankuang
1717 posts
juliankuang
#5 h  Jun 11, 2021, 5:19 PM • 1 Y
Y by centslordm
It's 3. $ $
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biscuit02
636 posts
biscuit02
#7 h  Jun 12, 2021, 8:27 AM
Y by
greenturtle3141 wrote:
In that case, even if you do find the ship, you'll need at least 5 more shots to sink it. Either way this makes the problem much more complicated and the solution is no longer necessarily optimal.

Yeah, you are right.
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zby
1873 posts
zby
#8 h  Jun 12, 2021, 2:08 PM
Y by
centslordm wrote:
ayo its 3

ayo just instruct your friend to watch the oppenent ships and tell you using hand signs
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juliankuang
1717 posts
juliankuang
#9 h  Jun 14, 2021, 4:55 PM
Y by
or sit opposite a mirror
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zby
1873 posts
zby
#10 h  Jun 15, 2021, 3:31 PM
Y by
yeah that works to0
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parmenides51
30629 posts
parmenides51
#11 h  Jun 16, 2021, 6:53 PM
Y by
min shots are 19 , official solution here in Russian (page 3/4)
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Wang2020
273 posts
Wang2020
#12 h  Jun 16, 2021, 6:56 PM
Y by
zby wrote:
yeah that works to0

I mean yeah technically the "min" is three as you can get the first shot right. And guess where the rest of the ship is right not the next two. But you will need 19 as max since when shooting the other two "spots" on the ship, you may miss the direction.
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tigerzhang
351 posts
tigerzhang
#13 h  Jun 25, 2021, 2:09 AM • 1 Y
Y by Bradygho
This problem is kind of broken if it assumes that you know how to play battleship; I don't, and I think many people won't either (especially considering that you have to hit all the cells, not just one, as people originally thought)
This post has been edited 1 time. Last edited by tigerzhang, Jun 25, 2021, 2:10 AM
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