quasi heron
Four circles are arranged as shown in the illustration. The numbers 1, 2, 3, ..., 10 (each a different number) must be entered into the ten areas created within the circles so that the sum of the numbers within each circle is the same. What is the highest possible value of this sum?
(A) 28
(B) 30
(C) 32
(D) 35
(E) 37
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ashen frost
@quasi heron Did you figure it out
quasi heron
<@670270374503776275> Did you figure it out
i mean trying to fill it out or smth but im tryna find like a way
to solve these problems more efficient
any tips?
ashen frost
any tips?
I think its 35 but my train of thought I am not sure of
so basically the largest possible sum of a circle would be 40
which is 10, 9, 8, 7, 6
But if you have one circle with 40 you will not be able to have any other circle with sum of 40 as well
so you will have to decrease that a bit
we decrease it by the number of regions that are outside of a circle which is 5
so 35
ashen frost
hmm
quasi heron
hmm
so i think the outer 3 circle parts has contain the highest numbers 8, 9 and 10
because the middle circle contains of 7 numbers
so if 8, 9 and 10 are gone we have 1, 2, 3, 4, 5,6,7 left
which we can somehow fill in for the middle circle
which adds up to 28
limpid merlin
W venn diagram (ik its not true but still)
ashen frost
which adds up to 28
but thats just trial an error right
quasi heron
but thats just trial an error right
yea but theoretically it makes sense
ashen frost
so i think the outer 3 circle parts has contain the highest numbers 8, 9 and 10
cuz I would think one should put the largest numbers in the centers so that we can get to the largest sum possible in all circles no?