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phosgene
phosgene
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Mathematica - 246 characters (no bonuses claimed)

f[x_,y_]:=x-y g[x_,y_]:=x/y h[x_,y_]:=x^(1/y) j[x_,y_]:=FromDigits@Join[IntegerDigits@x,{y}] z[{r_,n_,L_}]:=z[{L[[1]][r,n],n,Rest@L}] z[{r_,n_,{}}]:=r a[n_,t_]:=Union@Select[z[{n,n,#}]&/@Tuples[{Plus,f,Times,g,Power,h,j},t-1],IntegerQ@#&&0<#<11&]

Explanation

Function j concatenates two numbers digit-wise.

Function z takes a result r, number n, and list of functions L, each which operates on two arguments. It then applies the list of functions sequentially to argumnts [r,n][r,n] using recursion, until the list is empty, whereupon it returns the result.

Function a takes a number n and a number of copies t. It creates all tuples of length (t-1) from the list of functions {Plus, f, Times, g, Power, h, j} and sends each tuple through function z, then returns a list of all numbers 1 through 10 that were created.

Example execution a[2,3] returning {1, 2, 3, 6, 8}.

Limitations

Because the list of functions is applied sequentially, consuming one copy of the number each time, it can miss some combinations. For example, when operating on four twos, it would miss 22/22 = 1 due to its inability to evaluate the list of functions out of order. Of course, 2/2*2/2 = 1 covers this case.

Mathematica - 246 characters (no bonuses claimed)

f[x_,y_]:=x-y g[x_,y_]:=x/y h[x_,y_]:=x^(1/y) j[x_,y_]:=FromDigits@Join[IntegerDigits@x,{y}] z[{r_,n_,L_}]:=z[{L[[1]][r,n],n,Rest@L}] z[{r_,n_,{}}]:=r a[n_,t_]:=Union@Select[z[{n,n,#}]&/@Tuples[{Plus,f,Times,g,Power,h,j},t-1],IntegerQ@#&&0<#<11&]

Explanation

Function j concatenates two numbers digit-wise.

Function z takes a result r, number n, and list of functions L, each which operates on two arguments. It then applies the list of functions sequentially to argumnts [r,n] using recursion, until the list is empty, whereupon it returns the result.

Function a takes a number n and a number of copies t. It creates all tuples of length (t-1) from the list of functions {Plus, f, Times, g, Power, h, j} and sends each tuple through function z, then returns a list of all numbers 1 through 10 that were created.

Example execution a[2,3] returning {1, 2, 3, 6, 8}.

Limitations

Because the list of functions is applied sequentially, it can miss some combinations. For example, when operating on four twos, it would miss 22/22 = 1 due to its inability to evaluate the list of functions out of order. Of course, 2/2*2/2 = 1 covers this case.

Mathematica - 246 characters (no bonuses claimed)

f[x_,y_]:=x-y g[x_,y_]:=x/y h[x_,y_]:=x^(1/y) j[x_,y_]:=FromDigits@Join[IntegerDigits@x,{y}] z[{r_,n_,L_}]:=z[{L[[1]][r,n],n,Rest@L}] z[{r_,n_,{}}]:=r a[n_,t_]:=Union@Select[z[{n,n,#}]&/@Tuples[{Plus,f,Times,g,Power,h,j},t-1],IntegerQ@#&&0<#<11&]

Explanation

Function j concatenates two numbers digit-wise.

Function z takes a result r, number n, and list of functions L, each which operates on two arguments. It then applies the list of functions sequentially to argumnts [r,n] using recursion, until the list is empty, whereupon it returns the result.

Function a takes a number n and a number of copies t. It creates all tuples of length (t-1) from the list of functions {Plus, f, Times, g, Power, h, j} and sends each tuple through function z, then returns a list of all numbers 1 through 10 that were created.

Example execution a[2,3] returning {1, 2, 3, 6, 8}.

Limitations

Because the list of functions is applied sequentially, consuming one copy of the number each time, it can miss some combinations. For example, when operating on four twos, it would miss 22/22 = 1 due to its inability to evaluate the list of functions out of order. Of course, 2/2*2/2 = 1 covers this case.

Source Link
phosgene
phosgene
  • 1.2k
  • 10
  • 15

Mathematica - 246 characters (no bonuses claimed)

f[x_,y_]:=x-y g[x_,y_]:=x/y h[x_,y_]:=x^(1/y) j[x_,y_]:=FromDigits@Join[IntegerDigits@x,{y}] z[{r_,n_,L_}]:=z[{L[[1]][r,n],n,Rest@L}] z[{r_,n_,{}}]:=r a[n_,t_]:=Union@Select[z[{n,n,#}]&/@Tuples[{Plus,f,Times,g,Power,h,j},t-1],IntegerQ@#&&0<#<11&]

Explanation

Function j concatenates two numbers digit-wise.

Function z takes a result r, number n, and list of functions L, each which operates on two arguments. It then applies the list of functions sequentially to argumnts [r,n] using recursion, until the list is empty, whereupon it returns the result.

Function a takes a number n and a number of copies t. It creates all tuples of length (t-1) from the list of functions {Plus, f, Times, g, Power, h, j} and sends each tuple through function z, then returns a list of all numbers 1 through 10 that were created.

Example execution a[2,3] returning {1, 2, 3, 6, 8}.

Limitations

Because the list of functions is applied sequentially, it can miss some combinations. For example, when operating on four twos, it would miss 22/22 = 1 due to its inability to evaluate the list of functions out of order. Of course, 2/2*2/2 = 1 covers this case.