Brain Teasers Box Puzzles
Magic Square Puzzle problem — PLEASE HELP?
My son has been a puzzle to solve the box 9. It has three horizontal rows and vertical. He is using only the numbers 1-9 (once each) to get the answer. The boxes are letters in the top row as A, B, C, boxes in the middle row are letters D, E, F, and the boxes on the bottom row are letters G, H, I. The problem is that the teacher has told them so that you have successfully completed the following must be true: the sum of cells A, B, D, E should be 13 the sum of the squares D, E, G, H must be 24 the sum of the boxes B, C, E, F should be 21 the sum of the E boxes, F, H, I must be 18 We worked on a while and can get everyone to work, but a growing body. Can you help?
First, this is not truly a "magic square", because the rows and columns do not add to the same amounts. If it is estimated that reaching the wrong result. They give you the amounts for each one of the quadrants: upper left ABDE = = 13 = DEGH BCEF lower left = 24 = Top Right = 21 = EFHI bottom right = 18 The first thing to note is that adding opposing quadrants (ie bottom left and top right) ends with: D + E + G + H + B + C + E + F = 24 + 21 = 45 We also know that all the seats add to 45 (because 1 + 2 + … + 9 = 45): Write two equations: At + B + C + D + E + F + G + H + I = 45 B + C + D + 2E + F + G + H = 45 Subtract that you get: A – E + I = 0 A + I EE = = A + I In other words, E is the sum of A and I. Do the same with the other diagonal quadrants: A + B + D + 2E + F + H + I = 13 + 18 = 31 A + B + C + D + E + F + G + H + I = 45 Subtracting: E - C – G = 31 to 45 E – C – G = -14 E = C + G – 14 So you have E is the sum of two digits (A + I) and also 14 less than the sum of two digits others (C + G – 14). The smaller amount can be created with two digits is 1 + 2 = 3 The largest sum that can create with two digits is 8 + 9 = 17 The difference is 14. The only way to E for both is the sum of two digits (A + I) and 14 less than the sum of two digits other (C + G) where E is 3. This means that A and I are each 1 or 2, and C and G are each 8 or 9. So far have: ABC D 3 F GHI A, I = [1.2], C, G = [8.9] As to the lower right square: E + F + H + I = 18 E 3 F + H + I = 15 which is 1 or F 2 + H is 14 or 13. You may not use 8 or 9, because they are accustomed. You can not use 7 +7 = 14, because that would repeat a digit. Then, F and H should be 7 and 6, and must be 2. So far it has: 1 AC 3 F GH D 2 C, G = [8.9] F, H = [6.7] B, D = [4.5] We know that D + E + G + H = 24 And since E = 3, D + G + H = 21 If G is 8 or 9, then D + H = 13 or 12 . Possible values of D and H are: D = [4.5] H = [6.7] We can not make a sum of 13, only 12 (D = 5, H = 7). So G must be 9, C must be 8, H must be 7, D should be 5, B is 4 and F is 6. Answer: 1 4 8 5 3 6 9 7 2
Triangulator wood brain teaser puzzle
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