hugomimihu

so say t is total eggs

t<=150

t is odd

2 more than multiple of 3, or 1 less than multiple of 3

3 more than multiple of 4, or 1 less than of 4

4 more than of 5, or 1 less

5 more than of 6, or 1 less

Multiple of 7

 multiples of 7 to 150

7,14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119,126,133,140,147

Two more than multiples of 3

21-2 = 19, no

35-2=33, huh. 

49-2 = 47, no

63-2=61, no

77-2 = 75, huh.

91-2 = 89, no

105-2=103, no

119-2 = 117, huh.

Rest are no's.

35, 77, 119

35-3= 32, huh.         

77-3 = 75, huh.

119-3 = 116, huh.

35-4 = 31, no.

77 - 4 = 73, no

119-4 = 115, yes.

119.

Just to check, 119-5 = 114,/6 = 19, yes, and it's a multiple of 7,

Apologies for my prior mistake and thanks for bringing this to my attention, please check to ensure correctness.

What have you done so far?

In the future, please post the AoPS question you are most stuck with.

Funny I was crunching on these earlier today...

For the first... I'll give a hint

By triangle inequality we have

\(\begin{align*} n + 18 &> 25, \\ n + 25 &> 18, \\ 18 + 25 &> n, \end{align*}\)

Also, maybe search these up.

Typically AoPS questions are asked very often, and are answered.

BTW are you in 2387? The one with Hokaj?