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i signed up in 2013

There's an additional answer. Can anyone find it?

this is correct but can you prove it?

Using the numbers 0 through 9 (each once) place them on the vertices so that each triangle (the ones with the letters not the upside down triangles) add up to the same value. If possible.

You may already know that 1+2+3+4+5=15. Let's try five other consecutive integers: 14+15+16+17+18=80. How about -1+0+1+2+3=5? We might guess that the sum of 5 consecutive integers is divisible by 5. That turns out to be true. Maybe the sum of n consecutive integers is divisible by n. That turns out not to be true: 1+2 is not divisible by 2. Question: When is the sum of n consecutive integers divisible by n, and when is it not divisible by n?

very good point plasmid, the way i wrote the op is that he only eats apples if he has them so i made a mistake when i made my previous post. now the other answer is close if he was eating to drive.

Eric, jon, Latonia, Sam were playing a game known as the doubling game. The game gets its name from its unique pay out system. Each time a lloser is declared, they must double the amount of money everyone else had. So if Eric loses, and jon has 5 dollars and Sam has 8 dollars then he would give them each $5 and $8 respectively. At the end of round 1 Latonia loss At the end of round 2 Sam loss At the end of round 3 Eric loss At the end of round 4 jon loss By the end of round 4, all had 32 dollars. How much did they have at the start of the game?

Yes, but preordained doesnt = pointless

There is an 8x8 board where two diagonally opposing corners are removed making only 62 squares. You have only 31 dominoes which are 2x1 squares ( or 1x2). How can you place these dominoes so that the board is covered completely?

All are winners!

then intuitively would then intuitively, wouldn't the same logic apply in reverse? A husband knowing the frugal nature of his wife believes with very much certainty that his necktie was bought heavily discounted and thus has a great chance of winning

1) phil1882 2) Panther (And mine too ) 3) BMAD

Yes, but for returning also he would need to eat apples So, if he goes 500KM, he would eat 500 while going and 500 while coming back. very very close. consider the fact that the store he delivers to accepts and sells parts of apples to

i believe that this is the sum of a different sequence

is there another approach?

i like this approach. What is your reasoning?

you are adding the actual numbers. Like what Witzar did is what is asked for. 10,000 becomes 1 (since 1+0+0+0+0 = 1) and 9,999 becomes (36 since 9 +9 +9 +9 = 36) change all of the numbers in this manner, then add them up. but rather then simply doing brute force calculations or using coding, how can we quickly find this solution

hahaha. Essentially what Bonanova and some others have noted about this puzzle is pretty much correct. If one were to run repeated simulations you would see this kind of hive/honeycomb formations occur with an occasional loose pieces.

all of us here are still learning, i believe. which is why I believe we come to a site dedicated to challenge how we think.

Modifed though, as the circle is within your circle. Also if it rotates from 12 to 3, 3 to 6, 6 to 9 and comes back to start, that is four rotations, right? Yes, modified; yet similar. Both require the consideration that traversing a circular path (inside or out) affects the coin/circle in the same way that a rotation does, as it traverses that path. No, not four rotations - see k-man's picture. A rotation occurs each time the point p returns to its initial azimuth. Not each time the point p touches the outer circle. nicely done! I forgot to consider, in my own calculation, that the point p touches the circle more often than it does coming back to its starting position. which makes sense since it goes to the line before it comes back to its starting position on every spin.

using the sequence of numbers from 1 to 10,000, sum the digits together and rewrite the numbers as a new sequence. For example: ......., 345, 346, 347, ....., 5088, 5089, becomes ........., 12, 13, 14, ......, 21, 22 find a systematic approach or shortcut to adding the numbers from this second sequence without brute force calculations.

I reserve the right to make changes before the game starts . Host: Y-san Roster: 1. BMAD 2. 3. 4. 5. 6. 7. I think I may be the only one who doesn't get these mafia games but I will give it a shot....hopefully I don't die first