#include <bits/stdc++.h>
using namespace std;
const int N=100010;
int path[10];
bool vis[10];
int ans=0;
int backup[10];
int n;

int calc(int l, int r) {
  int res = 0;
  for (int i = l; i <= r; i++) {
    res = res * 10 + path[i];
  }
  return res;
}

void dfs(int u)
{
    if (u==10)
    {
        // for (int i=1;i<=9;i++) cout<<path[i]<<' ';
        // cout<<endl;
        memcpy(backup,path,sizeof(path));
        // for (int i=1;i<=9;i++) path[i]+=path[i-1];
        for (int i=1;i<=7;i++)
        {
            for (int j=i+1;j<=8;j++)
            {
                // int a=path[i],b=path[j]-path[i],c=path[9]-path[j];
                // cout<<a<<' '<<b<<' '<<c<<endl;
                int a = calc(1, i);
                int b = calc(i + 1, j);
                int c = calc(j + 1, 9);
                if (n*c==a*c+b) ans++;
            }
        }
        memcpy(path,backup,sizeof(backup));
        return;
    }
    for (int i=1;i<=9;i++)
    {
        if (!vis[i])
        {
            vis[i]=true;
            path[u]=i;
            dfs(u+1);
            vis[i]=false;
        }
    }
}
void solve()
{
    cin>>n;
    dfs(1);
    cout<<ans;
}

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int t=1;
    // cin>>t;
    while (t--)
    {
        solve();
    }
}

暴力：注释的错因是当成前缀和了，但是这不是累加各个数字，而是应该当成一个大的数

优化版

#include <bits/stdc++.h>
using namespace std;
const int N=100010;
#define int long long
int n;
int ans;
bool vis[10];
bool backup[10];
bool check(int a,int c)
{
    int b=c*(n-a);
    if (!a||!b||!c) return false;
    memcpy(backup,vis,sizeof(vis));
    while (b)
    {
        int x=b%10;
        if(!x || backup[x]) return false;
        backup[x]=true;
        b/=10;
    }
    for (int i=1;i<=9;i++)
    {
        if (backup[i]==false) return false;
    }
    return true;
}
void dfs_c(int u, int a, int c)
{
    if(u > 9) return;

    if(check(a,c)) ans++;

    for(int i = 1; i <= 9; i++)
    {
        if(!vis[i])
        {
            vis[i] = true;
            dfs_c(u + 1, a, c * 10 + i);
            vis[i] = false;
        }
    }
}
void dfs_a(int u, int a)
{
    if(a >= n) return;
    if(a) dfs_c(u, a, 0);

    for(int i = 1; i <= 9; i++)
    {
        if(!vis[i])
        {
            vis[i] = true;
            dfs_a(u + 1, a * 10 + i);
            vis[i] = false;
        }
    }
}
void solve()
{
    cin>>n;
    dfs_a(0,0);//用了0个数，现在a的值为0
    cout<<ans;
}

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int t=1;
    // cin>>t;
    while (t--)
    {
        solve();
    }
}