数学竞赛题,1到9只用加与减算出结果为26

来源:百度知道 编辑:UC知道 时间:2024/05/26 11:37:34

答案是从1到9只用加与减算出26是不可能的。
下面是我的证明:
1、如果两个整数的和是偶数,那么这两个数的奇偶性相同。
2、因为(A+B)+(A-B)=2A是偶数,由结论1可以推出A+B和A-B奇偶性相同(A、B为整数)。
3、1+2+3+4+5+6+7+8+9=45是奇数,所以由结论2可以推出,用1到9这九个数(每个数用而且只用一次)进行任意的加减运算得到的数都与45的奇偶性相同,只能是奇数。故所以得出用1到9只用加与减算出26是不可能的。

Private Sub Form_Click()
Dim i(1 To 10) As Integer
Dim l(1 To 10) As Integer
Dim j As Integer
For j = 1 To 10
l(j) = j
Next j
Dim sum As Integer
Dim i1, i2, i3, i4, i5, i6, i7, i8, i9, i10
For i1 = -1 To 1 Step 2
For i2 = -1 To 1 Step 2
For i3 = -1 To 1 Step 2
For i4 = -1 To 1 Step 2
For i5 = -1 To 1 Step 2
For i6 = -1 To 1 Step 2
For i7 = -1 To 1 Step 2
For i8 = -1 To 1 Step 2
For i9 = -1 To 1 Step 2
For i10 = -1 To 1 Step 2
sum = i1 * l(1) + i2 * l(2) + i3 * l(3) + i4 * l(4) + i5 * l(5) + i6 * l(6) + i7 * l(7) + i8 * l(8) + i9 * l(9) + i10 * l(10)
Print i1 * l(1) & " + " & i2 * l(2) & " + " & i3 * l(3) & &