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Bunuel
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The function f(x) represents the number of ways that prime numbers can 04 Dec 2019, 01:01
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45% (02:34) correct 55% (02:47) wrong based on 259 sessions

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The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8


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rajatchopra1994
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The function f(x) represents the number of ways that prime numbers can Updated on: 04 Dec 2019, 02:03
Originally posted by rajatchopra1994 on 04 Dec 2019, 01:12.
Last edited by rajatchopra1994 on 04 Dec 2019, 02:03, edited 1 time in total.
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Bunuel
The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8


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Explanation:
F(12)=
2+2+2+2+2+2------1
2+2+2+3+3-----2
2+2+3+5----3
2+3+7-----4
3+3+3+3-----5
5+7-----6
2+5+5-----7 (Corrected)

Total = 7
F(12)=7

IMO-D

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The function f(x) represents the number of ways that prime numbers can 04 Dec 2019, 01:55
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One more 5+5+2 , total 7

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The function f(x) represents the number of ways that prime numbers can 17 Oct 2021, 01:05
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The function f(x) represents the number of ways that prime numbers can 19 Oct 2021, 10:51
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The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8
Show more

The total number of possibilities are :

1-7+5
2-7+3+2
3-5+3+2+2
4-5+5+2
5-2+2+2+2+2+2
6-3+3+3
7-3+2+3+2

Therefore IMO D
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The function f(x) represents the number of ways that prime numbers can 19 Oct 2021, 23:35
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YZLIM1994
Bunuel

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The prime numbers should be summed up to 12, so they should all be less than 12. Note them, they are 2, 3, 5, 7, 11... Can leave out 11 since 11+1 is not possible as 1 is not a prime (neither a composite).

Now start splitting 12...

1. 12 = 6x2. One possibility.
2. 10+2 = 5+5+2 and 2+3+5+2 and 2+3+2+3+2 (don't worry about the ordering). So 3 possibilities.
3. 9+3 = 3x4 + 3 and 2+7+3 and 2+5+2+3 and 2+2+3+2+3... 3 more possibilities.
4. 7+5... this is a repeat of 10+2... so leave it out.

Total possibilities = 1+3+3 = 7
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The function f(x) represents the number of ways that prime numbers can 09 Jan 2025, 09:17
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The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d... where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5.

What is f(12)?

12 = 2+2+2+2+2+2 = 2+2+2+3+3 = 3+3+3+3 = 2+2+3+5 = 2+5+5 = 2+3+7 = 5+7

f(12) = 7

IMO D
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