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abdulhakeem 2025-01-30 23:44:12 -06:00
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reasoning_gym/data/gsm_data/p2/0008.json Normal file
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{
"question": "A juggler can juggle 16 balls. Half of the balls are golf balls, and half of the golf balls are blue. How many blue golf balls are there?",
"answer": "Golf Balls:16/2=<<16/2=8>>8\nBlue Golf Balls:8/2=<<8/2=4>>4 balls\n#### 4",
"id_orig": 269,
"id_shuffled": 8,
"question_annotated": "A juggler can juggle {n, 16} balls. {frac_1, half} of the balls are {ball_type, golf} balls, and the rest are {ball_type2,tennis} balls. {frac_2,half} of the {ball_type,golf} balls are {color, blue}, of which {frac_3, half} are marked. {frac_22,half} of the {ball_type2,tennis} balls are {color2,green}, and all except {frac_33,half} of those {color2,green} balls are marked. How many marked balls are there in total?\n\n#init:\n- ball_type, ball_type2 = sample([\"golf\", \"tennis\"], 2)\n- color, color2 = sample(colors,2)\n- $frac_1 = sample(fractions)\n- $frac_2 = sample(fractions)\n- $frac_22 = sample(fractions)\n- $frac_3 = sample(fractions)\n- $frac_33 = sample(fractions)\n- $n = range(120, 601, 20)\n\n#conditions:\n- is_int(n * frac_1 * frac_2 * frac_3)\n- is_int(n * (1-frac_1) * frac_22 * (1-frac_33))\n\n#answer: int(n * frac_1 * frac_2 * frac_3) + int(n * (1-frac_1) * frac_22 * (1-frac_33))",
"answer_annotated": "{ball_type} balls: {n} * {frac_1}=<<{n}*{frac_1}={n*frac_1}>>{int(n*frac_1)}\n{ball_type2} balls: {n} * {frac_1}=<<{n}*{1-frac_1}={n*(1-frac_1)}>>{int(n*(1-frac_1))}\n\n{color} {ball_type} balls:{int(n*frac_1)}*{frac_2}=<<{int(n*frac_1)}*{frac_2}={int(n*frac_1*frac_2)}>>{int(n*frac_1*frac_2)} balls.\n{color2} {ball_type2} balls:{int(n*(1-frac_1))}*{frac_2}=<<{int(n*(1-frac_1))}*{frac_2}={int(n*(1-frac_1)*frac_2)}>>{int(n*(1-frac_1)*frac_2)} balls.\n\nThe marked {ball_type} balls are {int(n*frac_1*frac_2)} * {frac_3} = {int(int(n*frac_1*frac_2) * frac_3)}.\nThe marked {ball_type2} balls are {int(n*(1-frac_1)*frac_22)} * {1-frac_33} = {int(n*(1-frac_1)*frac_22*(1-frac_33))}.\n\nTotal marked balls: {int(int(n*frac_1*frac_2) * frac_3)} + {int(n*(1-frac_1)*frac_22*(1-frac_33))} = {int(int(n*frac_1*frac_2) * frac_3) + int(n*(1-frac_1)*frac_22*(1-frac_33))}\n#### {int(int(n*frac_1*frac_2) * frac_3) + int(n*(1-frac_1)*frac_22*(1-frac_33))}"
}