## Sort numeric values based on proximity to a given number

The image above demonstrates an array formula in cell C25 that extracts numbers based on how far off they are from the number in cell C22. Example, 9 and 11 are closest to 10 and are extracted first.

Array formula in C25:

### How to create an array formula

- Copy (Ctrl + c) and paste (Ctrl + v) array formula into formula bar.
- Press and hold Ctrl + Shift.
- Press Enter once.
- Release all keys.

Copy cell C25 and paste it down as far as needed.

### Explaining array formula

**Step 1 - Find k-th smallest difference to the value in C22**

=INDEX($B$25:$B$37, MATCH(**SMALL(ABS($B$25:$B$37-$C$22);ROW(A1)), **(COUNTIF($B$25:$B$37, $B$25:$B$37)<>COUNTIF($D$24:D24, $B$25:$B$37))*ABS($B$25:$B$37-$C$22), 0))

SMALL(ABS($B$25:$B$37-$C$22), ROW(A1))

becomes

SMALL(ABS({1;3;4;7;8;11;11;14;15;17;18;19;20}-10), ROW(A1))

becomes

SMALL({9;7;6;3;2;1;1;4;5;7;8;9;10}, 1)

and returns 1.

**Step 2 - Calculate valid numbers**

=INDEX($B$25:$B$37, MATCH(SMALL(ABS($B$25:$B$37-$C$22);ROW(A1)), **(COUNTIF($B$25:$B$37, $B$25:$B$37)<>COUNTIF($D$24:D24, $B$25:$B$37))*ABS($B$25:$B$37-$C$22), **0))

(COUNTIF($B$25:$B$37, $B$25:$B$37)<>COUNTIF($D$24:D24, $B$25:$B$37))*ABS($B$25:$B$37-$C$22)

becomes

(COUNTIF({1;3;4;7;8;11;11;14;15;17;18;19;20}, {1;3;4;7;8;11;11;14;15;17;18;19;20})<>COUNTIF("Sorted closest to farthest to 10", {1;3;4;7;8;11;11;14;15;17;18;19;20}))*ABS({1;3;4;7;8;11;11;14;15;17;18;19;20}-10)

becomes

({1;1;1;1;1;2; 2;1;1;1;1;1;1}<>{0;0;0;0;0; 0;0;0;0;0;0;0;0})*ABS({1;3;4;7;8;11;11; 14;15;17;18;19;20}-10)

becomes

({1;1;1;1;1;2; 2;1;1;1;1;1;1}<>{0;0;0;0;0; 0;0;0;0;0;0;0;0})*ABS({1;3;4;7;8;11;11; 14;15;17;18;19;20}-10)

becomes

({TRUE;TRUE;TRUE;TRUE;TRUE; TRUE;TRUE;TRUE;TRUE;TRUE; TRUE;TRUE;TRUE})*{9;7;6;3;2;1;1;4;5;7;8;9;10}

and returns

{9;7;6; 3;2;1; 1;4;5; 7;8;9; 10}

**Step 3 - Match k-th smallest difference to valid numbers**

=INDEX($B$25:$B$37, **MATCH(SMALL(ABS($B$25:$B$37-$C$22);ROW(A1)), (COUNTIF($B$25:$B$37, $B$25:$B$37)<>COUNTIF($D$24:D24, $B$25:$B$37))*ABS($B$25:$B$37-$C$22), 0)**)

MATCH(SMALL(ABS($B$25:$B$37-$C$22);ROW(A1)), (COUNTIF($B$25:$B$37, $B$25:$B$37)<>COUNTIF($D$24:D24, $B$25:$B$37))*ABS($B$25:$B$37-$C$22), 0)

becomes

MATCH(1,{9;7;6; 3;2;1; 1;4;5; 7;8;9; 10}, 0)

returns 6.

**Step 4 - Return a value of the cell at the intersection of a particular row and column**

=INDEX($B$25:$B$37, MATCH(SMALL(ABS($B$25:$B$37-$C$22);ROW(A1)), (COUNTIF($B$25:$B$37, $B$25:$B$37)<>COUNTIF($D$24:D24, $B$25:$B$37))*ABS($B$25:$B$37-$C$22), 0))

becomes

=INDEX($B$25:$B$37, 6)

becomes

=INDEX({1;3;4;7;8;11;11;14;15;17;18;19;20}, 6)

returns number 11.

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