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{
"problem": "Find the difference between $1000_7$ and $666_7$ in base $7$.",
"level": "Level 4",
"type": "Number Theory",
"solution": "Setting up the subtraction and borrowing as shown: $$\\begin{array}{c@{}c@{}c@{}c@{}c} &&&&\\\\ &\\cancelto{0}{1}&\\cancelto{6}{0}&\\cancelto{6}{0}&{\\cancelto{7}{0}}_{7}\\\\ &-&6&6&6_7\\\\ \\cline{2-5} &&&&1_7.\\\\ \\end{array}$$So the difference is $\\boxed{1_7}$."
} |