Still experimenting

reasoning_gym/data/gsm_data/p2/0004.json

@@ -0,0 +1,8 @@
+{
+  "question": "Garrett is popping popcorn for a snack. As the pan of kernels heats up, the kernels start popping faster. Twenty pop in the first 30 seconds of cooking, then three times that amount in the next 30 seconds. The kernels increase to four times the initial popping rate in the next thirty seconds, but in the final 30 seconds, the popping slows down to half the rate as the past 30 seconds. After Garrett takes the pan off the heat, a quarter of the number of kernels that popped in the final 30 seconds of cooking also pop from the residual heat. How many pieces of popcorn does Garrett have to eat?",
+  "answer": "In the second 30 seconds of cooking, 3 * 20 = <<3*20=60>>60 kernels pop.\nIn the third 30 seconds, 4 * 20 = <<4*20=80>>80 kernels pop.\nIn the final 30 seconds, 80 / 2 = <<80/2=40>>40 kernels pop.\nAfter cooking, the residual heat makes 40 / 4 = <<40/4=10>>10 kernels pop.\nThus, Garrett has 20 + 60 + 80 + 40 + 10 = <<20+60+80+40+10=210>>210 pieces of popcorn to eat.\n#### 210",
+  "id_orig": 1264,
+  "id_shuffled": 4,
+  "question_annotated": "{name,Garrett} is popping popcorn for a snack. As the {p, pan} of kernels heats up, the kernels start popping faster. {n,20} pop in the first {sec, 30} seconds of cooking, then {k_2,3} times that amount in the next {sec, 30} seconds. The kernels increase to {k_3, 4} times the initial popping rate in the next {sec, 30} seconds. In the final {sec, 30} seconds, the popping slows down to half the rate as the past {sec, 30} seconds. After {name,Garrett} takes the {p, pan} off the heat, a quarter of the number of kernels that popped in the final {sec, 30} seconds of cooking also pop from the residual heat. {name,Garret} gives {frac,third} of the made popcorn to his brother {name2,James}. How many more pieces of popcorn does {name,Garrett} have to eat than his brother?\n\n\n#init:\n- name, name2 = sample(names_male, 2)\n- p = sample(['pan', 'pot', 'skillet'])\n- $n = range(10, 101, 10)\n- $sec = range(10, 31, 2)\n- $k_2 = range(2, 5)\n- $k_3 = range(3, 8)\n- $frac = sample(fraction_alnum)\n\n#conditions:\n- k_3 > k_2\n- frac < 0.5\n- divides(k_3 * n, 8)\n- is_int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8) ) * (1-frac))\n\n\n#answer: int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8) ) * (1-frac))-int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8))*frac)",
+  "answer_annotated": "In the second {sec} seconds of cooking, {k_2}* {n} = <<{k_2}*{n}={k_2*n}>>{k_2*n} kernels pop.\nIn the third {sec} seconds, {k_3} * {n} = <<{k_3}*{n}={k_3 * n}>>{k_3 * n} kernels pop.\nIn the final {sec} seconds, {k_3 * n} / 2 = <<{k_3*n}/2={k_3*n//2}>>{k_3*n//2} kernels pop.\nAfter cooking, the residual heat makes {k_3*n//2} / 4 = <<{k_3*n//2}/4={k_3*n//8}>>{k_3*n//8} kernels pop.\nThus, {name} has {n} + {k_2 * n} + {k_3 * n} + {k_3 * n // 2} + {k_3 * n // 8} = << {n} + {k_2 * n} + {k_3 * n} + {k_3 * n // 2} + {k_3 * n // 8}={n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8)}>>{n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8)} pieces of popcorn to eat.\nBut since {frac} of popcorn go to the brother, {n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8)} * {frac} = {int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8))*frac)}.\nThe remaining popcorn for {name} is {n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8)} * {1-frac} = {(n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8) ) * (1-frac)}.\nSo the differences is {int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8) ) * (1-frac))} - {int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8))*frac)} = {int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8) ) * (1-frac))-int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8))*frac)}\n\n#### {int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8) ) * (1-frac))-int((n + (k_2 * n + k_3 * n) + (k_3 * n // 2) + (k_3 * n // 8))*frac)}"
+}