- 24
- 9
Yes, sorry. In that case it will be 15 combinations.Well, four times 17, not three, but yes, this is the only solution.
Yes, sorry. In that case it will be 15 combinations.Well, four times 17, not three, but yes, this is the only solution.
3x3x3 = 27?There is a cube, constituted of 9 smaller ones, like Rubik's.
I avoided that since I feared endless discussions whether there is a cube at the center or not ...3x3x3 = 27?
I don't get it. There is only one number per corner, eight corners in total and six numbers at the center of the surfaces, namely the product of the four numbers in the corners, respectively.Let the corners be identified as (x,y,z) where a,b,c= 0 or 1.
Let (0,0,0)=(0,1,0)=(0,0,1)=-1 and use 1 for all other corners. There is one face (x=0) showing -1 from three -1 corners, two faces (y=0 and z=0) showing +1 from two -1 corners, two faces (y=1 and z=1) showing -1 from one -1 corner and one face (x=1) showing +1 from no -1 corner. Sum: -3+5-1+2-2+1 = 0
That's how I understood the puzzle. I made a calculation error, however. -3+5-1+2-2+1 = 2 not 0.There is only one number per corner, eight corners in total and six numbers at the center of the surfaces, namely the product of the four numbers in the corners, respectively.
Yes. As several members use coding to solve problems ...118:We transform xy to x0y, which means we add 90*x. xy must be a factor of 90*x. Note that 90=2*3*3*5. Trivially x0 becomes x00 after multiplication by 10, I don't list these in the following:
x=1: xy=15 (becomes 105 after multiplying by 7), 18 (becomes 108 after multiplying by 6)
x=2: -
x=3: -
x=4: 45 (becomes 405 after multiplying by 9)
x=5: -
x=6: -
x=7: -
x=8: -
x=9: -
Hmm.. just casework.
Is there a winning strategy for one of the players?
Sorry, typo.#119
With only 3004 cards dealt out of 3040, this is not a perfect information game.
Yes.Is there a somewhat easy strategy to follow?
If I understand the question correctly then the best I found is covering the E column one by one, saving half of the field. If you let it go into E then it will spread both vertically and towards the larger columns and you can only keep one side from spreading in both directions.120. We have ##64## hectares of a square forest, say they are numerated like the chess board. At twelve o'clock a fire starts on ##D1##. Firefighters can secure one hectare from burning every hour. Every next hour, the fire spreads to all horizontally or vertically neighboured hectares (no diagonals). How many hectares can be saved at best?
D120
You can save more than 50% for burning.If I understand the question correctly then the best I found is covering the E column one by one, saving half of the field. If you let it go into E then it will spread both vertically and towards the larger columns and you can only keep one side from spreading in both directions.
Am I to understand it does NOT spread to the smaller columns ? Please clarify this spreading (e.g. after D1 it can spread to D2 and to E1 -- not to C1 ?)Fresh said:it will spread both vertically and towards the larger columns