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prompts/cot/gsm8k.md

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+Question: There are 15 trees in the grove. Grove workers will plant trees in the grove today. After they are done, there will be 21 trees. How many trees did the grove workers plant today?
+Answer: There are 15 trees originally. Then there were 21 trees after some more were planted. So there must have been 21 - 15 = 6. The answer is 6.
+
+Question: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot?
+Answer: There are originally 3 cars. 2 more cars arrive. 3 + 2 = 5. The answer is 5.
+
+Question: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total?
+Answer: Originally, Leah had 32 chocolates. Her sister had 42. So in total they had 32 + 42 = 74. After eating 35, they had 74 - 35 = 39. The answer is 39.
+
+Question: Jason had 20 lollipops. He gave Denny some lollipops. Now Jason has 12 lollipops. How many lollipops did Jason give to Denny?
+Answer: Jason started with 20 lollipops. Then he had 12 after giving some to Denny. So he gave Denny 20 - 12 = 8. The answer is 8.
+
+Question: Shawn has five toys. For Christmas, he got two toys each from his mom and dad. How many toys does he have now?
+Answer: Shawn started with 5 toys. If he got 2 toys each from his mom and dad, then that is 4 more toys. 5 + 4 = 9. The answer is 9.
+
+Question: There were nine computers in the server room. Five more computers were installed each day, from monday to thursday. How many computers are now in the server room?
+Answer: There were originally 9 computers. For each of 4 days, 5 more computers were added. So 5 * 4 = 20 computers were added. 9 + 20 is 29. The answer is 29.
+
+Question: Michael had 58 golf balls. On tuesday, he lost 23 golf balls. On wednesday, he lost 2 more. How many golf balls did he have at the end of wednesday?
+Answer: Michael started with 58 golf balls. After losing 23 on tuesday, he had 58 - 23 = 35. After losing 2 more, he had 35 - 2 = 33 golf balls. The answer is 33.
+
+Question: Olivia has $23. She bought five bagels for $3 each. How much money does she have left?
+Answer: Olivia had 23 dollars. 5 bagels for 3 dollars each will be 5 x 3 = 15 dollars. So she has 23 - 15 dollars left. 23 - 15 is 8. The answer is 8.

prompts/cot/math.md

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+Question: Kevin Kangaroo begins hopping on a number line at 0. He wants to get to 1, but he can hop only $\frac{1}{3}$ of the distance. Each hop tires him out so that he continues to hop $\frac{1}{3}$ of the remaining distance. How far has he hopped after five hops? Express your answer as a common fraction.
+Answer: Let's think step by step
+Kevin hops $1/3$ of the remaining distance with every hop.
+His first hop takes $1/3$ closer.
+For his second hop, he has $2/3$ left to travel, so he hops forward $(2/3)(1/3)$.
+For his third hop, he has $(2/3)^2$ left to travel, so he hops forward $(2/3)^2(1/3)$.
+In general, Kevin hops forward $(2/3)^{k-1}(1/3)$ on his $k$th hop.
+We want to find how far he has hopped after five hops.
+This is a finite geometric series with first term $1/3$, common ratio $2/3$, and five terms.
+Thus, Kevin has hopped $\frac{\frac{1}{3}\left(1-\left(\frac{2}{3}\right)^5\right)}{1-\frac{2}{3}} = \boxed{\frac{211}{243}}$.
+The answer is \frac{211}{243}}
+
+
+Question: What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+3$?
+Answer: Let's think step by step
+We rewrite the equation as $x^2 + 14x + y^2 - 4y = 10$ and then complete the square,
+resulting in  $(x+7)^2-49 + (y-2)^2-4=10$,
+or $(x+7)^2+(y-2)^2=63$.
+This is the equation of a circle with center $(-7, 2)$ and radius $\sqrt{63},$
+so the area of this region is $\pi r^2 = \boxed{63\pi}$.
+The answer is 63\pi
+
+
+Question: If $x^2+y^2=1$, what is the largest possible value of $|x|+|y|$?
+Answer: Let's think step by step
+If $(x,y)$ lies on the circle,
+so does $(x,-y),$ $(-x,-y),$ and $(-x,-y),$ (which all give the same value of $|x| + |y|$),
+so we can assume that $x \ge 0$ and $y \ge 0.$
+Then $|x| + |y| = x + y.$  Squaring, we get
+\[(x + y)^2 = x^2 + 2xy + y^2 = 1 + 2xy.\]
+Note that $(x - y)^2 \ge 0.$
+Expanding, we get $x^2 - 2xy + y^2 \ge 0,$ so $2xy \le x^2 + y^2 = 1.$
+Hence,\[1 + 2xy \le 2,\]which means $x + y \le \sqrt{2}.$
+Equality occurs when $x = y = \frac{1}{\sqrt{2}},$
+so the maximum value of $|x| + |y|$ is $\boxed{\sqrt{2}}.$
+The answer is \sqrt{2}
+
+
+Question: If $f(x)=\frac{ax+b}{cx+d}, abcd\not=0$ and $f(f(x))=x$ for all $x$ in the domain of $f$, what is the value of $a+d$?
+Answer: Let's think step by step
+The condition $f(f(x))$ means that $f$ is the inverse of itself,
+so its graph is symmetrical about the line $y = x$.
+With a rational function of this form, we will have two asymptotes:
+a vertical one at $x=-d/c$ if $cx+d$ does not divide $ax+b$,
+and a horizontal one at $y=a/c$,
+if we take the limit of $f(x)$ as $x$ goes to $\pm\infty$.
+In order for $f$ to be its own inverse, the intersection of the asymptotes must lie on the line $y=x$
+so that it and its asymptotes reflect onto themselves.
+This means that $-d/c=a/c$,
+and therefore $-d=a$ and $a+d=\boxed{0}$.
+The answer is 0
+
+
+Question: A math teacher requires Noelle to do one homework assignment for each of the first five homework points she wants to earn; for each of the next five homework points, she needs to do two homework assignments; and so on, so that to earn the $n^{\text{th}}$ homework point, she has to do $n\div5$ (rounded up) homework assignments. For example, when she has 11 points, it will take $12\div5=2.4\rightarrow3$ homework assignments to earn her $12^{\text{th}}$ point. What is the smallest number of homework assignments necessary to earn a total of 25 homework points?
+Answer: Let's think step by step
+Noelle only has to do 1 homework assignment to earn her first point,
+and the same is true for each of her first five points.
+She must then do 2 homework assignments to earn her sixth point, seventh point, and so on, up to her tenth point.
+Continuing, we see that Noelle must do a total of \[1+1+1+1+1+2+2+2+2+2+\dots+5+5+5+5+5\] homework assignments to earn 25 points.
+This sum may be rewritten as $5(1+2+3+4+5)=5(15)=\boxed{75}$.
+The answer is 75
+
+
+Question: The quadratic equation $x^2+mx+n=0$ has roots that are twice those of $x^2+px+m=0,$ and none of $m,$ $n,$ and $p$ is zero. What is the value of $n/p?$
+Answer: Let's think step by step
+Let $r_1$ and $r_2$ be the roots of $x^2+px+m=0.$
+Since the roots of $x^2+mx+n=0$ are $2r_1$ and $2r_2,$ we have the following relationships: \[
+m=r_1 r_2,\quad n=4r_1 r_2,\quad p=-(r_1+r_2), \quad\text{and}\quad
+m=-2(r_1+r_2).
+\] So \[
+n = 4m, \quad p = \frac{1}{2}m,
+\quad\text{and}\quad
+\frac{n}{p}=\frac{4m}{\frac{1}{2}m}=\boxed{8}.
+\]
+Alternatively, the roots of \[
+\left(\frac{x}{2}\right)^2 + p\left(\frac{x}{2}\right) + m = 0
+\] are twice those of $x^2 + px + m = 0.$
+Since the first equation is equivalent to $x^2 + 2px + 4m = 0,$
+we have \[m = 2p \quad\text{and}\quad n = 4m, \quad\text{so}\quad \frac{n}{p} = \boxed{8}.\]
+The answer is 8
+
+
+Question: Expand $(2z^2 + 5z - 6)(3z^3 - 2z + 1)$.
+Answer: Let's think step by step
+$$\begin{array}{crrrrrrr}
+& & & 3z^3 & & -2z & + 1 & \\
+\times & & & & 2z^2 & +5z & -6 \\
+\cline{1-7}\rule{0pt}{0.17in}
+& & & -18z^3 & & +12z & -6 & \\
+& & +15z^4 & & -10z^2 & +5z & & \\
++ & 6z^5 & & -4z^3 & +2z^2 & & & \\
+\cline{1-7}\rule{0pt}{0.17in}
+& 6z^5 & +15z^4 & -22z^3 & - 8z^2 &+17z & -6 &
+\end{array}$$
+The answer is 6z^5+15z^4-22z^3-8z^2+17z-6}
+
+
+Question: Find the mean of all solutions for $x$ when $x^3 + 3x^2 - 10x = 0$.
+Answer: Let's think step by step
+First, we factor the equation as $x(x^2 +3x - 10) = 0$.
+So, one solution is $x=0$ and the other two solutions are the solutions to $x^2 + 3x-10=0$.
+We could either factor the quadratic, or note that the sum of the solutions to this quadratic is $-(3/1)=-3$,
+so the mean of the three solutions to the original equation is $-3/3=\boxed{-1}$.
+The answer is -1

prompts/pal/gsm8k.md

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+Let's write a plan based on the python program for solving math problems.
+
+<|user|>
+Question: 
+Richard lives in an apartment building with 15 floors. Each floor contains 8 units, and 3/4 of the building is occupied. What's the total number of unoccupied units In the building?
+
+Program:
+```python
+def solution():
+    num_floors = 15
+    num_units_per_floor = 8
+    num_total_floors = num_floors * num_units_per_floor
+    num_units_occupied = num_floors * num_units_per_floor * 0.75
+    num_units_unoccupied = num_total_floors - num_units_occupied
+    return num_units_unoccupied
+```
+
+<|assistant|>
+Plan: To solve the problem follow these steps:
+1. Determine the total number of units in the building. We can multiply the number of units per floor by the total number of floors.
+2. Determine the number of occupied units. We can multiply the total number of units by the fraction representing the occupied units.
+3. Determine the number of unoccupied units. We can subtract the number of occupied units from the total number of units.
+
+---
+
+<|user|>
+Question: 
+A robe takes 2 bolts of blue fiber and half that much white fiber.  How many bolts in total does it take?
+
+Program:
+```python
+def solution():
+    """A robe takes 2 bolts of blue fiber and half that much white fiber.  How many bolts in total does it take?"""
+    blue_fiber = 2
+    white_fiber = blue_fiber / 2
+    total_fiber = blue_fiber + white_fiber
+    return total_fiber
+```
+
+<|assistant|>
+Plan: To solve the problem follow these steps:
+1. Determine the amount of white fiber needed, which is half the amount of the blue fiber.
+2. Determine the total number of bolts. We can add the bolts of blue fiber to the bolts of white fiber.
+
+---
+
+<|user|>
+Question: 
+Janet’s ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins for her friends every day with four. She sells the remainder at the farmers' market daily for $2 per fresh duck egg. How much in dollars does she make every day at the farmers' market?
+
+Program:
+```python
+def solution():
+    """Janet\u2019s ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins for her friends every day with four. She sells the remainder at the farmers' market daily for $2 per fresh duck egg. How much in dollars does she make every day at the farmers' market?"""
+    eggs_per_day = 16
+    eggs_eaten_per_day = 3
+    eggs_baked_per_day = 4
+    eggs_sold_per_day = eggs_per_day - eggs_eaten_per_day - eggs_baked_per_day
+    eggs_sold_price = 2
+    eggs_sold_dollars = eggs_sold_per_day * eggs_sold_price
+    return eggs_sold_dollars
+```
+
+<|assistant|>
+Plan: To solve the problem follow these steps:
+1. Determine the number of eggs Janet sells each day. We can subtract the eggs used for breakfast and muffins from the total eggs laid.
+2. Determine Janet's daily earnings at the farmers' market. We can multiply the number of eggs she sells by the price per egg.
+
+---

prompts/pal/gsm8k_cot.md

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+Let's follow the hint and use python to solve math problems.
+
+Question: 
+Richard lives in an apartment building with 15 floors. Each floor contains 8 units, and 3/4 of the building is occupied. What's the total number of unoccupied units In the building?
+
+Hint: To solve the problem follow these steps:
+Calculate the total number of units in the building. Multiply the number of units per floor by the total number of floors.
+Determine the number of occupied units. Multiply the total number of units by the fraction representing the occupied units.
+Find the number of unoccupied units. Subtract the number of occupied units from the total number of units.
+
+Program:
+```python
+def solution():
+    num_floors = 15
+    num_units_per_floor = 8
+    num_total_floors = num_floors * num_units_per_floor
+    num_units_occupied = num_floors * num_units_per_floor * 0.75
+    num_units_unoccupied = num_total_floors - num_units_occupied
+    return num_units_unoccupied
+```
+
+---
+
+Question: 
+A robe takes 2 bolts of blue fiber and half that much white fiber.  How many bolts in total does it take?
+
+Hint: To solve the problem follow these steps:
+Calculate the amount of white fiber needed. It's half the amount of the blue fiber.
+Determine the total number of bolts required. Add the bolts of blue fiber to the bolts of white fiber.
+
+Program:
+```python
+def solution():
+    """A robe takes 2 bolts of blue fiber and half that much white fiber.  How many bolts in total does it take?"""
+    blue_fiber = 2
+    white_fiber = blue_fiber / 2
+    total_fiber = blue_fiber + white_fiber
+    return total_fiber
+```
+
+---
+
+Question: 
+Janet’s ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins for her friends every day with four. She sells the remainder at the farmers' market daily for $2 per fresh duck egg. How much in dollars does she make every day at the farmers' market?
+
+Hint: To solve the problem follow these steps:
+Calculate the number of eggs Janet sells each day. Subtract the eggs used for breakfast and muffins from the total eggs laid.
+Determine Janet's daily earnings at the farmers' market. Multiply the number of eggs she sells by the price per egg.
+
+Program:
+```python
+def solution():
+    """Janet\u2019s ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins for her friends every day with four. She sells the remainder at the farmers' market daily for $2 per fresh duck egg. How much in dollars does she make every day at the farmers' market?"""
+    eggs_per_day = 16
+    eggs_eaten_per_day = 3
+    eggs_baked_per_day = 4
+    eggs_sold_per_day = eggs_per_day - eggs_eaten_per_day - eggs_baked_per_day
+    eggs_sold_price = 2
+    eggs_sold_dollars = eggs_sold_per_day * eggs_sold_price
+    return eggs_sold_dollars
+```
+
+---

prompts/pal/gsm8k_mkplan1.md

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+Let's write a plan based on the solution and the python program for solving math problems.
+
+<|user|>
+Question: 
+Richard lives in an apartment building with 15 floors. Each floor contains 8 units, and 3/4 of the building is occupied. What's the total number of unoccupied units In the building?
+
+Solution:
+The total number of units in the building will be 8 units/floor * 15 floors = <<8*15=120>>120 units.
+If 3/4 of the building is occupied, then the total number of occupied units is 3/4 * 120 units = <<3/4*120=90>>90 units.
+The total number of unoccupied units is 120 units - 90 units = <<120-90=30>>30 units.
+
+Program:
+```python
+def solution():
+    num_floors = 15
+    num_units_per_floor = 8
+    num_total_floors = num_floors * num_units_per_floor
+    num_units_occupied = num_floors * num_units_per_floor * 0.75
+    num_units_unoccupied = num_total_floors - num_units_occupied
+    return num_units_unoccupied
+```
+
+<|assistant|>
+Plan: To solve the problem follow these steps:
+1. Determine the total number of units in the building. We can multiply the number of units per floor by the total number of floors.
+2. Determine the number of occupied units. We can multiply the total number of units by the fraction representing the occupied units.
+3. Determine the number of unoccupied units. We can subtract the number of occupied units from the total number of units.
+
+---
+
+<|user|>
+Question: 
+A robe takes 2 bolts of blue fiber and half that much white fiber.  How many bolts in total does it take?
+
+Solution:
+It takes 2/2=<<2/2=1>>1 bolt of white fiber
+So the total amount of fabric is 2+1=<<2+1=3>>3 bolts of fabric
+
+Program:
+```python
+def solution():
+    """A robe takes 2 bolts of blue fiber and half that much white fiber.  How many bolts in total does it take?"""
+    blue_fiber = 2
+    white_fiber = blue_fiber / 2
+    total_fiber = blue_fiber + white_fiber
+    return total_fiber
+```
+
+<|assistant|>
+Plan: To solve the problem follow these steps:
+1. Determine the amount of white fiber needed, which is half the amount of the blue fiber.
+2. Determine the total number of bolts. We can add the bolts of blue fiber to the bolts of white fiber.
+
+---
+
+<|user|>
+Question: 
+Janet’s ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins for her friends every day with four. She sells the remainder at the farmers' market daily for $2 per fresh duck egg. How much in dollars does she make every day at the farmers' market?
+
+Solution:
+Janet sells 16 - 3 - 4 = <<16-3-4=9>>9 duck eggs a day.
+She makes 9 * 2 = $<<9*2=18>>18 every day at the farmer’s market.
+
+Program:
+```python
+def solution():
+    """Janet\u2019s ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins for her friends every day with four. She sells the remainder at the farmers' market daily for $2 per fresh duck egg. How much in dollars does she make every day at the farmers' market?"""
+    eggs_per_day = 16
+    eggs_eaten_per_day = 3
+    eggs_baked_per_day = 4
+    eggs_sold_per_day = eggs_per_day - eggs_eaten_per_day - eggs_baked_per_day
+    eggs_sold_price = 2
+    eggs_sold_dollars = eggs_sold_per_day * eggs_sold_price
+    return eggs_sold_dollars
+```
+
+<|assistant|>
+Plan: To solve the problem follow these steps:
+1. Determine the number of eggs Janet sells each day. We can subtract the eggs used for breakfast and muffins from the total eggs laid.
+2. Determine Janet's daily earnings at the farmers' market. We can multiply the number of eggs she sells by the price per egg.
+
+---