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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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generic whiteboard problem
ostriches88   19
N 14 minutes ago by happypi31415
Source: 2024 AMC10B p16
Jerry likes to play with numbers. One day, he wrote all the integers from $1$ to $2024$ on the whiteboard. Then he repeatedly chose four numbers on the whiteboard, erased them, and replaced them with either their sum or their product. (For example, Jerry's first step might have been to erase $1, 2, 3$, and $5$, and then write either $11$, their sum, or $30$, their product, on the whiteboard.) After repeatedly performing this operation, Jerry noticed that all the remaining numbers on the board were odd. What is the maximum possible number of integers on the board at that time?

$
\textbf{(A) }1010 \qquad
\textbf{(B) }1011 \qquad
\textbf{(C) }1012 \qquad
\textbf{(D) }1013 \qquad
\textbf{(E) }1014 \qquad
$
19 replies
ostriches88
Nov 13, 2024
happypi31415
14 minutes ago
Problem 2
evt917   46
N 31 minutes ago by AbhayAttarde01
Source: 2024 AMC 12B #2 / AMC 10B #2
What is $10! - 7! \cdot 6!$?

$
\textbf{(A) }-120 \qquad
\textbf{(B) }0 \qquad
\textbf{(C) }120 \qquad
\textbf{(D) }600 \qquad
\textbf{(E) }720 \qquad
$
46 replies
evt917
Nov 13, 2024
AbhayAttarde01
31 minutes ago
No more topics!
10a vs 10b
golden_star_123   125
N Today at 5:17 AM by wuwang2002
Post the difference between your 10a and 10b score!
125 replies
golden_star_123
Nov 13, 2024
wuwang2002
Today at 5:17 AM
10a vs 10b
G H J
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golden_star_123
130 posts
#1 • 1 Y
Y by ranu540
Post the difference between your 10a and 10b score!
Z K Y
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megarnie
5307 posts
#2
Y by
34.5 but it was 12a and 10b
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pingpongmerrily
2424 posts
#3
Y by
golden_star_123 wrote:
Post the difference between your 10a and 10b score!

10b greater by 13.5
Z K Y
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andrewcheng
482 posts
#4
Y by
10b by 16.5
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Existing_Human1
120 posts
#5
Y by
10b - 16.6

10 b = 103.5
10 a = 87

Shows how there isn't really a big difference between 20 points
Z K Y
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cdm
234 posts
#6
Y by
133.5/141, so 7.5
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Elephant200
1451 posts
#7
Y by
My scores were very similar - 112.5 on A and 109.5 on B
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Squidget
372 posts
#8
Y by
10b improved by 10.5
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pingpongmerrily
2424 posts
#9
Y by
Existing_Human1 wrote:
10b - 16.6

10 b = 103.5
10 a = 87

Shows how there isn't really a big difference between 20 points

or it shows that 10b was insanely easy
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pieMax2713
4131 posts
#10
Y by
12a/12b 109.5/121.5, 12 difference
couldve been 118.5/132 though
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TiguhBabeHwo
208 posts
#11
Y by
126-126 $ $
Z K Y
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ostriches88
1441 posts
#12
Y by
10b higher by 25.5 :blush:
This post has been edited 1 time. Last edited by ostriches88, Nov 13, 2024, 6:33 PM
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Andrew2019
2218 posts
#13
Y by
112.5 - 78 = 34.5
Z K Y
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meduh6849
313 posts
#14
Y by
0
10a and 12b
Z K Y
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mathprodigy2011
58 posts
#15
Y by
10a and 12b

difference(4.5)

did better on 12b lol(I sold 10a)
This post has been edited 1 time. Last edited by mathprodigy2011, Nov 13, 2024, 6:40 PM
Reason: .
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