A171223 Solutions to place plus, minus, multiply or divide signs to a nonzero digits sequence 123456789 so that result of thus described arithmetic operation will be n.

161, 151, 127, 152, 129, 123, 135, 135, 149, 162, 157, 140, 134, 131, 150, 129, 134, 140, 161, 156, 126, 134, 143, 122, 123, 150, 137, 146, 141, 131

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Example

For n=1, a(1)=161 means there exist 161 solutions as following: Solution 1: 1-2/3*45+6+7+8+9=1 Solution 2: 12-34+5-6+7+8+9=1 Solution 3: 1-2+34-56+7+8+9=1 Solution 4: 1*2-3*4-5+6-7+8+9=1 Solution 5: 1*2+3-4*5+6-7+8+9=1 Solution 6: 1-2-3-4+5-6-7+8+9=1 Solution 7: 1+2+3-4-5-6-7+8+9=1 Solution 8: 1*2*3-4-5-6-7+8+9=1 Solution 9: 1*2-3*4*5+6*7+8+9=1 ......... Solution 151: 12*3/4*56/7/8/9=1 Solution 152: 1*2-3-45-6*7+89=1 Solution 153: 1-23-4+5-67+89=1 Solution 154: 1*2-3-4*5-67+89=1 Solution 155: 1+23-45-67+89=1 Solution 156: 1*23+4+56+7-89=1 Solution 157: 123-4*5-6-7-89=1 Solution 158: 123+4-5*6-7-89=1 Solution 159: 123+4+5-6*7-89=1 Solution 160: 1+23+4-5+67-89=1 Solution 161: 1-23+45+67-89=1

Prog

(Excel) VBA Program:
Sub Test() Dim Solutions(1 To 500), result As Single Dim temp As Long, x(1 To 17) As String, op Dim i As Long, j As Long, out As String, num As Long op = Array("+", "-", "*", "/", "") For i = 1 To 9 x(2 * i - 1) = i Next For i = 0 To 5 ^ 8 - 1 temp = i For j = 1 To 8 x(2 * j) = op(temp Mod 5) temp = temp \ 5 Next out = Join(x, "") result = Evaluate(out) If result > 0 Then If result < 501 Then If InStr(result, ".") = 0 Then Solutions(result) = Solutions(result) + 1 End If End If End If Next Debug.Print Join(Solutions, vbCrLf) End Sub

Crossrefs

Sequence in context: A027553 A159378 A172074 * A278896 A249397 A025350

Adjacent sequences: A171220 A171221 A171222 * A171224 A171225 A171226

Keyword

easy,base,nonn

Author

Zhining Yang, Dec 05 2009

Status

approved