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8 lines
No EOL
1.7 KiB
JSON
8 lines
No EOL
1.7 KiB
JSON
{
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"question": "A plague infects ten people. Every day, each infected person infects six others. How many people are infected after three days?",
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"answer": "On the first day, the original ten people infect six people each, so 10 * 6 = <<10*6=60>>60 more people are infected.\nThere are 10 + 60 = <<10+60=70>>70 infected people after the first day.\nOn the second day, 70 * 6 = <<70*6=420>>420 more people are infected.\nThere are 70 + 420 = <<70+420=490>>490 infected people after the second day.\nOn the third day, 490 * 6 = 2940 more people are infected. Therefore, there are 490 + 2940 = 3430 infected people after three days.\n#### 3430",
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"id_orig": 858,
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"id_shuffled": 98,
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"question_annotated": "A new {disease,plague} infects {n0,10} people. Every day, each infected person infects {r,6} others. How many people are infected after {d,3} days?\n\n#init:\n- disease = sample(['virus', 'bacteria', 'parasite', 'infection'])\n- $n0 = range(3, 31)\n- $r = range(2, 5)\n- $d = range(2, 8)\n\n#conditions:\n- n0 * (r + 1)**d < 5000\n\n#answer: n0 * (r + 1)**d",
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"answer_annotated": "On the first day, the original {n0} people infect {r} people each, so {n0}*{r}=<<{n0}*{r}={n0*r}>>{n0*r} more people are infected.\nThere are {n0}+{n0*r}=<<{n0}+{n0*r}={n0+n0*r}>>{n0+n0*r} infected people after the first day.\nOn the second day, {n0+n0*r}*{r}=<<{n0+n0*r}*{r}={(n0+n0*r)*r}>>{(n0+n0*r)*r} more people are infected.\nThere are {n0+n0*r}+{(n0+n0*r)*r}=<<{n0+n0*r}+{(n0+n0*r)*r}={n0+n0*r+(n0+n0*r)*r}>>{n0+n0*r+(n0+n0*r)*r} infected people after the second day.\nWe see that every day, the amount of infected people will be multiplied by {r+1} (from {n0} to {n0*(r+1)} to {n0*(r+1)*(r+1)}). So, we will have {n0 * (r + 1)**d} infected people after {d} days.\n#### {n0 * (r + 1)**d}"
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} |