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jasen last won the day on November 30 2016
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Arrange numbers and operators to the magic triangle
jasen replied to jasen's question in New Logic/Math Puzzles
When creating this puzzle (using computer), I started with 3 first constraints, then I got many solutions, so I have to add 1 more constraint. But I have to keep the symmetry of the puzzle. First I tried to sum the three corners, but I still got some solutions. Then I tried to product the three corners, which yields 1 unique solution. When creating this puzzle (using computer), I started with 3 first constraints, then I got many solutions, so I have to add 1 more constraint. But I have to keep the symmetry of the puzzle. First I tried to sum the three corners, but I still got some solutions. Then I tried to product the three corners, which yields 1 unique solution. 
Replace letters with numbers 1 to 9, so the 3 operations are equals
jasen posted a question in New Logic/Math Puzzles
Replace letters with numbers 1 to 9, so the 3 operations below are equals. Each letter represents one unique number. ab / c = de * f = gh  i Note : If a = 1, and b = 2, then ab = 12 NOT multiplication It is more fun if you solve this without computer, trust me this is easy. 
based on this @bonanova puzzle, I create another similar puzzle You are given the following ten statements and are asked to determine a particular number. At least one of statements 7 and 8 is true. This either is the first true or the first false statement. The number is a prime number. The first true statement multiplied by the last false statement divides the number. The number of divisors of the number is greater than the sum of the numbers of the true statements. The number has exactly 4 prime divisors. The number is bigger than 1000. The numbers of true statements do not equal the numbers of false statement One of the divisors is a cube number bigger than 1. There are 3 consecutive False statements and 3 consecutive True statements.

yes there are still 2 more solution.

Arrange numbers and operators to the magic triangle
jasen replied to jasen's question in New Logic/Math Puzzles
Yes you are right, each operator only can be used once. making ((9!)(6!))/3 cases. (Because of the symmetry) 
Arrange numbers and operators to the magic triangle
jasen posted a question in New Logic/Math Puzzles
Note : A # B = A*10 + B Arrange the numbers 1 to 9 to green triangles, and arrange operator (+,,x,/,^, and #) to the white triangles, so the math operations below are equals. (((A op1 B) op2 D) op4 F) = constant (((F op4 G) op5 H) op6 I) = constant (((I op6 E) op3 C) op1 A) = constant A x F x I = constant 
Reverse the order of 8 poisonous substances
jasen replied to jasen's question in New Logic/Math Puzzles
No, you can choose the robot in each step something like 2213232..... 
Interesting 3x3 table, to form a numbers of unique prime numbers
jasen replied to jasen's question in New Logic/Math Puzzles

8 very poisonous substances named s1 to s8 are kept in a safety room. The substances are kept in ascending order (s1,s2,s3,s4,s5,s6,s7 and s8). In the room there are 3 robots. First robot can "rotate left" the order of the substances. If the order is (a,b,c,d,e,f,g,h) the robot will make it (b,c,d,e,f,g,h,a) Second robot can split the substances into 2 part then reverse the order of each part. If the order is (a,b,c,d,e,f,g,h) the robot will make it (d,c,b,a,h,g,f,e) But the robot is a bit broken, so the resulting order is a bit wrong. The resulting order will become (d,c,a,b,h,g,f,e). Third robot can split the substances into 4 part then reverse the order of each part If the order is (a,b,c,d,e,f,g,h) the robot will make it (b,a,d,c,f,e,h,g) Questions If the 2nd robot is not broken, how many minimum step needed by using the robots to reverse the order into descending order? Show the steps! After the 2nd robot is broken, how many minimum step needed by using the robots to reverse the order into descending order? Show the steps!

Interesting 3x3 table, to form a numbers of unique prime numbers
jasen replied to jasen's question in New Logic/Math Puzzles
It is possible, I have it. I will show it next week if nobody find it until 10 Nov 2016. 
Interesting 3x3 table, to form a numbers of unique prime numbers
jasen posted a question in New Logic/Math Puzzles
151 131 359 131 151 \ ^ ^ ^ / 131 < 1 3 1 > 131 353 < 3 5 3 > 353 191 < 1 9 1 > 191 / V V V \ 151 131 953 131 151 This 3x3 table have an interesting properties. Every direction (up,down, Right, Left, 45°,135°,225°,315°) of 3 cell form prime numbers. There are 6 unique prime numbers from this table, they are 131, 151, 191, 353, 359, 953. Create a more interesting 3x3 table with the same rule, which there are 9 unique prime numbers from the table. 
Example : abc / \ / \ d e f g / \ / \ hijkl \ / \ / m n o p \ / \ / qrs a+b+c = a+e+j = c+f+j = 23, and so on.... Note : There are 2 solutions, if we rule out reflections and rotations. Bonus Puzzle : How if all the rows of 3 numbers between O (big o) sums to 22,24,25,26,27,28,29,31,32,33,34,35,36, 37, and 38. I have checked all the solutions by computer, and all those sums have solutions.

Interesting pattern on 5x5 table which has unique properties
jasen posted a question in New Logic/Math Puzzles
[0,1,6,4,3] [4,5,6,0,9] [9,9,0,1,1] [1,0,4,5,6] [7,6,4,9,0] This 5x5 table has unique properties. Each number in a cell means : or Here is another example [0,1,6,4,8] [1,2,1,3,2] [1,0,9,0,1] [4,5,6,0,4] [4,5,1,0,9] [6,5,9,5,6] [4,4,0,6,6] [3,3,0,7,7] [5,5,0,5,5] [1,0,4,5,1] [1,0,9,5,6] [9,0,1,0,9] [2,1,4,4,0] [8,7,9,8,9] [4,5,1,5,4] What surprised me is, every table like this will follow this : I have checked this with my computer. Why this happens ? 
Solve this alphametic ENLIST + SILENT + LISTEN = ANAGRAM Leading zero is ok. There is only 1 solution.