Monday Madness

i'm waiting for oldman to find the answer.. haven't had much free time so not going to get the answer myself before monday, so looks like it might be another one that rolls over to next week unless someone else can get the answer soon. i'm going to guess it's a circle shape i just haven't had the time to sit down and work out how big the circle needs to be.

ok i'm going to go with circle and area of 54.9726. this is all guess work using 10 balls for the outer ring, don't know if the extra 5 balls would fit inside it, but hope so. my logic may be way off but i figure 10 balls in a circle would give me a circumference of 20 inches to the centre of the balls, so knowing the circumference i worked out the radius to be 3.1831, now to get the circumference of the outer edge of the balls i just added 1 inch to the 3.1831 radius of the smaller circle. we now have a radius of 4.1831 from which i worked out the area of the outer circle to be 54.9726. square inches. was thinking the circle might need to be squished into an oval shape for the balls to fit inside, but if so then i think the area would still be the same as a circle, (hope so anyway. ). so my second answer would be oval and area of 54.9726

Terry,

I am unable to make the balls fit into the circle you described. "Squishing" the circle into an oval is also unsuccessful.

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well it was a guess.. i tried 11 balls for the outer ring but think the area was bigger than even the 60 square inches of a line. did have a shape like in those drawings but with the extra ball on top to make an arrow type shape but never worked out the area of that for some reason, but to be honest i'm running out of ideas.

ok think i have the correct lengths for all the sides of that arrow head shape, just need to have the time to do a bit of googling to find out how i work out the area so will get back to this problem later when i have more time. 8.3094 8.3094 5.1547 5.1547 3.1547

Like this?

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yes , exactly like that, if my calcs are correct.

my last idea would be a 6 sided shape each with 3 balls, and 2 in the middle, but i need to re-learn how to work out the area.

Like this?

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well i calculated an area of 55.467812 for that. so smallest so far if i'm correct with my calcs.

I made it 55.4863 but close enough.

Well done terry1966! That is the shape and size that I came up with also. So far no one else has provided anything smaller… so I think you have it!

How about some pumpkin pie?
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i think i deserve it after all that hard work.. to be honest i don't even remember learning about shapes, area's, etc in the first place, most things jog my memory somewhat but nothing about this puzzle did. so think this was the hardest monday madness you've come up with for me.