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05AB1E, 24 22 bytes F•žNjεEÿ¶^²è+%•5¡sèS}g Amount of hops as first input, and the starting digit as second input. Try it online or verify all test cases (except for the one with 20 hops, which times …

Java 8, 137 129 91 89 bytes int f(int n,int k){return--n<0?1:k%2>0?k==5?0:f(n,2)+f(n,4):2*f(n,k>0?1:4)+k/4%2*f(n,0);} Port of @Arnauld's JavaScript answer, provided by @OlivierGrégoire. -2 byte than …

05AB1E, 16 bytes Ç®X‚xâDí«δ+çJ˜.M Inspired by @mousetail's comment! Try it online or verify all test cases. Explanation: Ç # Convert the (implicit) input-triplet of strings to pairs of their …

Java 10, 631 608 606 597 578 504 489 475 470 bytes s->{int i=0,k,d,n,x,y,l,e[],f[];var m=new boolean[81];for(var p:s.split(",")){e=f=new int[81];e[40]=k=1;for(var P:p.split("\\.")){f=e.clone();k++;fo …

05AB1E, 41 bytes Ç`+É•wH˜OÝ•44в*s11%©è•2ĀpakΩÕðβ•₂в2ä+sè®è Try it online or verify all test cases. Explanation: Ç # Convert the (implicit) input to a list of codepoint integ …

Java 10, 336 330 287 285 282 276 bytes m->{var V=new java.util.HashMap();int i=64,A[]=new int[i];var t="";for(;i-->0;)t+=A[i]=(i%56<8?i%8*35%41%10%8+2:9>>i/16&1)*(i/32*2-1);V.put(t,1);for(var a:m){fo …

Java 11, 35 32 bytes s->(s+s).strip().chars().sum()/9 Port of @Joel's Python 3 answer. -3 bytes thanks to @Joel as well. Uses NULL-bytes (\0) for Rooks and tabs (\t) for spaces. Try it online. I tri …

05AB1E, 11 10 bytes 8Lã18δβƵz+ -1 byte thanks to @ovs. Try it online. A port of @JosephWalker's Python 3 answer is 11 bytes: 7ÝT+18*8LâO - Try it online. A port of @Arnauld's JavaScript first answer …

MathGolf, 12 bytes 8r♂+G*mÉ8╒+─ Try it online. Explanation: 8r # Push a list in the range [0,8) ♂+ # Add 10 to each to make the range [10,18) G* # Multiply each by 18 …

MathGolf, 9 bytes 2╤ç■gɱ~¡ Try it online. Explanation: 2╤ # Push a list in the range [-2,2]: [-2,-1,0,1,2] ç # Remove the 0 with a falsey filter ■ # Cartesian product with …

05AB1E, 29 bytes Çнθ<…BNR¹Åsk+.•7œΔ&‘•èI9*¹θα« Port of @tsh' JavaScript answer Inputs in the order notation,perspective, where the perspective is 1/0 for black/white respectively. Try it online or ve …

05AB1E, 69 68 bytes θDI¹->©н‚ß®W.ý`D¹н‚ß¹н¹ß)vyN4%N8«.Λ}1A0.ΛS¶¡¶δ.ø¬g¶иšĆ2Fø€ü3}εε˜¶KÙg Inputs as two loose pairs, in the order [queen x,queen y], [board width,board height]. Try it online or verify …

05AB1E, 37 36 bytes 56āÌ'fìâ„g4δšDí«ε`"1.ÿ eÿ 2.ÿ Qh4#", Try it online. If outputting as a list of lines is allowed, the trailing ", can be removed for -2 bytes: try it online. Explanation: 56 …

Whitespace, 380 378 bytes [S S S T S S S N _Push_n=8][N S S N _Create_Label_LOOP][S S S T N _Push_1][T S S T _Subtract:_n=n-1][S N S _Duplicate_n][N T T S N _If_negative_Jump_to_Label_EXIT][ …

05AB1E, 12 8 bytes αDËsP3‹~ -4 bytes porting AndrovT's Vyxal answer. Input as two pairs of codepoints. Try it online or verify all test cases or verify every single pair of chessboard positions. Orig …