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        "content": "So I've got this equation: 1 + 2 * 3 + 4 * 5 + 6 * 7 + 8 * 9 = 479, and it's supposed to be incorrect, but I need to add just one pair of parentheses to make it true. Hmm, let's see.\n\nFirst, I should probably understand what the equation is currently doing. In math, multiplication is performed before addition according to the order of operations (PEMDAS/BODMAS rules). So, in the expression 1 + 2 * 3 + 4 * 5 + 6 * 7 + 8 * 9, the multiplications would be calculated first, and then the additions.\n\nLet's compute it step by step without any parentheses:\n\nFirst, the multiplications:\n\n2 * 3 = 6\n\n4 * 5 = 20\n\n6 * 7 = 42\n\n8 * 9 = 72\n\nNow, plug these back into the equation:\n\n1 + 6 + 20 + 42 + 72\n\nNow, add them up:\n\n1 + 6 = 7\n\n7 + 20 = 27\n\n27 + 42 = 69\n\n69 + 72 = 141\n\nSo, without any parentheses, the equation equals 141, not 479. So, clearly, something needs to change.\n\nNow, I need to add one pair of parentheses to make this equal to 479. Parentheses can change the order of operations, so whatever is inside the parentheses gets calculated first.\n\nI need to think about where to place these parentheses to alter the result significantly, since 141 is quite a bit smaller than 479.\n\nMaybe I can group some additions and multiplications in a way that increases the result.\n\nLet me consider different placements:\n\nOption 1: (1 + 2) * 3 + 4 * 5 + 6 * 7 + 8 * 9\n\nCalculate inside the parentheses first:\n\n1 + 2 = 3\n\nThen, 3 * 3 = 9\n\nNow, the equation is: 9 + 4 * 5 + 6 * 7 + 8 * 9\n\nNext, multiplications:\n\n4 * 5 = 20\n\n6 * 7 = 42\n\n8 * 9 = 72\n\nSo, 9 + 20 + 42 + 72\n\nAdd them up:\n\n9 + 20 = 29\n\n29 + 42 = 71\n\n71 + 72 = 143\n\nStill not 479.\n\nOption 2: 1 + (2 * 3 + 4) * 5 + 6 * 7 + 8 * 9\n\nFirst, inside the parentheses:\n\n2 * 3 = 6\n\n6 + 4 = 10\n\nNow, multiply by 5: 10 * 5 = 50\n\nSo, the equation becomes: 1 + 50 + 6 * 7 + 8 * 9\n\nNext, multiplications:\n\n6 * 7 = 42\n\n8 * 9 = 72\n\nNow, add them up:\n\n1 + 50 = 51\n\n51 + 42 = 93\n\n93 + 72 = 165\n\nStill not 479.\n\nOption 3: 1 + 2 * (3 + 4) * 5 + 6 * 7 + 8 * 9\n\nFirst, inside the parentheses:\n\n3 + 4 = 7\n\nThen, 2 * 7 = 14\n\nThen, 14 * 5 = 70\n\nSo, the equation is: 1 + 70 + 6 * 7 + 8 * 9\n\nNext, multiplications:\n\n6 * 7 = 42\n\n8 * 9 = 72\n\nNow, add them up:\n\n1 + 70 = 71\n\n71 + 42 = 113\n\n113 + 72 = 185\n\nStill not 479.\n\nOption 4: 1 + 2 * 3 + 4 * (5 + 6) * 7 + 8 * 9\n\nFirst, inside the parentheses:\n\n5 + 6 = 11\n\nThen, 11 * 7 = 77\n\nSo, the equation is: 1 + 2 * 3 + 4 * 77 + 8 * 9\n\nNext, multiplications:\n\n2 * 3 = 6\n\n4 * 77 = 308\n\n8 * 9 = 72\n\nNow, add them up:\n\n1 + 6 = 7\n\n7 + 308 = 315\n\n315 + 72 = 387\n\nCloser, but still not 479.\n\nOption 5: 1 + 2 * 3 + 4 * 5 + 6 * (7 + 8) * 9\n\nFirst, inside the parentheses:\n\n7 + 8 = 15\n\nThen, 15 * 9 = 135\n\nSo, the equation is: 1 + 2 * 3 + 4 * 5 + 6 * 135\n\nNext, multiplications:\n\n2 * 3 = 6\n\n4 * 5 = 20\n\n6 * 135 = 810\n\nNow, add them up:\n\n1 + 6 = 7\n\n7 + 20 = 27\n\n27 + 810 = 837\n\nWay too big.\n\nHmm, 837 is much larger than 479. Maybe I need to reduce the impact of the parentheses.\n\nOption 6: 1 + 2 * (3 + 4 * 5) + 6 * 7 + 8 * 9\n\nFirst, inside the parentheses:\n\n3 + 4 * 5\n\nWait, in this case, multiplication comes before addition inside the parentheses, so 4 * 5 = 20, then 3 + 20 = 23\n\nThen, 2 * 23 = 46\n\nSo, the equation is: 1 + 46 + 6 * 7 + 8 * 9\n\nNext, multiplications:\n\n6 * 7 = 42\n\n8 * 9 = 72\n\nNow, add them up:\n\n1 + 46 = 47\n\n47 + 42 = 89\n\n89 + 72 = 161\n\nStill not 479.\n\nOption 7: 1 + 2 * 3 + 4 * (5 + 6 * 7) + 8 * 9\n\nFirst, inside the parentheses:\n\n5 + 6 * 7\n\nMultiplication first: 6 * 7 = 42, then 5 + 42 = 47\n\nThen, 4 * 47 = 188\n\nSo, the equation is: 1 + 2 * 3 + 188 + 8 * 9\n\nNext, multiplications:\n\n2 * 3 = 6\n\n8 * 9 = 72\n\nNow, add them up:\n\n1 + 6 = 7\n\n7 + 188 = 195\n\n195 + 72 = 267\n\nStill not 479.\n\nOption 8: 1 + 2 * 3 + 4 * 5 + 6 * (7 + 8 * 9)\n\nFirst, inside the parentheses:\n\n7 + 8 * 9\n\nMultiplication first: 8 * 9 = 72, then 7 + 72 = 79\n\nThen, 6 * 79 = 474\n\nSo, the equation is: 1 + 2 * 3 + 4 * 5 + 474\n\nNext, multiplications:\n\n2 * 3 = 6\n\n4 * 5 = 20\n\nNow, add them up:\n\n1 + 6 = 7\n\n7 + 20 = 27\n\n27 + 474 = 479\n\nPerfect! That equals 479.\n\nSo, by placing the parentheses around 7 + 8 * 9, and multiplying that sum by 6, we get the desired result.\n\nTherefore, the corrected equation is: 1 + 2 * 3 + 4 * 5 + 6 * (7 + 8 * 9) = 479\n\n**Final Answer**\n\n\\[ \\boxed{1 + 2 \\times 3 + 4 \\times 5 + 6 \\times (7 + 8 \\times 9) = 479} \\]",
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