Language: C++

#include <iostream>
#include <vector>
#include <tuple>
#include <algorithm>

int main()
{
	int N;
	std::cin >> N;

	std::vector<std::tuple<int, int, int>> data;
	int x, y, h;
	for (int i = 0; i < N; i++) {
		std::cin >> x >> y >> h;
		data.push_back(std::make_tuple(h, x, y));
	}

	std::sort(std::begin(data), std::end(data), std::greater<int>());

	int CX = 0;
	int CY = 0;
	int H = 0;

	bool find = false;
	for (int x = 0; x <= 100; x++) {
		for (int y = 0; y <= 100; y++) {
			for (int h = 0; h <= 200; h++) {
				int cx = x;
				int cy = y;
				int ch = std::get<0>(data[0]) + h;

				// すべての観測点で矛盾が生じなければＯＫ
				bool check = true;
				for (int i = 0; i < N; i++) {
					int ch = std::abs(cx - std::get<1>(data[i])) +
						std::abs(cy - std::get<2>(data[i])) +
						std::get<0>(data[i]);
					if (ch != H) {
						check = false;
						break;
					}
				}

				if (check) {
					CX = cx;
					CY = cy;
					H = ch;
					find = true;
					break;
				}
			}

			if (find) break;
		}
		if (find) break;
	}

	if (find) {
		std::cout << CX << " " << CY << " " << H << std::endl;
	}


	return 0;
}

Compiler output:
In file included from /usr/include/c++/14/bits/stl_algobase.h:71,
                 from /usr/include/c++/14/string:51,
                 from /usr/include/c++/14/bits/locale_classes.h:40,
                 from /usr/include/c++/14/bits/ios_base.h:41,
                 from /usr/include/c++/14/ios:44,
                 from /usr/include/c++/14/ostream:40,
                 from /usr/include/c++/14/iostream:41,
                 from a.cc:1:
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'constexpr bool __gnu_cxx::__ops::_Iter_comp_iter<_Compare>::operator()(_Iterator1, _Iterator2) [with _Iterator1 = __gnu_cxx::__normal_iterator<std::tuple<int, int, int>*, std::vector<std::tuple<int, int, int> > >; _Iterator2 = __gnu_cxx::__normal_iterator<std::tuple<int, int, int>*, std::vector<std::tuple<int, int, int> > >; _Compare = std::greater<int>]':
/usr/include/c++/14/bits/stl_algo.h:1777:14:   required from 'void std::__insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1777 |           if (__comp(__i, __first))
      |               ~~~~~~^~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1817:25:   required from 'void std::__final_insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1817 |           std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1908:31:   required from 'void std::__sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1908 |           std::__final_insertion_sort(__first, __last, __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:4805:18:   required from 'void std::sort(_RAIter, _RAIter, _Compare) [with _RAIter = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = greater<int>]'
 4805 |       std::__sort(__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
      |       ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:18:11:   required from here
   18 |         std::sort(std::begin(data), std::end(data), std::greater<int>());
      |         ~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h:158:30: error: no match for call to '(std::greater<int>) (std::tuple<int, int, int>&, std::tuple<int, int, int>&)'
  158 |         { return bool(_M_comp(*__it1, *__it2)); }
      |                       ~~~~~~~^~~~~~~~~~~~~~~~
In file included from /usr/include/c++/14/string:49:
/usr/include/c++/14/bits/stl_function.h:394:7: note: candidate: 'constexpr bool std::greater<_Tp>::operator()(const _Tp&, const _Tp&) const [with _Tp = int]'
  394 |       operator()(const _Tp& __x, const _Tp& __y) const
      |       ^~~~~~~~
/usr/include/c++/14/bits/stl_function.h:394:29: note:   no known conversion for argument 1 from 'std::tuple<int, int, int>' to 'const int&'
  394 |       operator()(const _Tp& __x, const _Tp& __y) const
      |                  ~~~~~~~~~~~^~~
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Val_comp_iter<_Compare>::operator()(_Value&, _Iterator) [with _Value = std::tuple<int, int, int>; _Iterator = __gnu_cxx::__normal_iterator<std::tuple<int, int, int>*, std::vector<std::tuple<int, int, int> > >; _Compare = std::greater<int>]':
/usr/include/c++/14/bits/stl_algo.h:1757:20:   required from 'void std::__unguarded_linear_insert(_RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Val_comp_iter<greater<int> >]'
 1757 |       while (__comp(__val, __next))
      |              ~~~~~~^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1785:36:   required from 'void std::__insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1785 |             std::__unguarded_linear_insert(__i,
      |             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~
 1786 |                                 __gnu_cxx::__ops::__val_comp_iter(__comp));
      |                                 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1817:25:   required from 'void std::__final_insertion_sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1817 |           std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1908:31:   required from 'void std::__sort(_RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1908 |           std::__final_insertion_sort(__first, __last, __comp);
      |           ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:4805:18:   required from 'void std::sort(_RAIter, _RAIter, _Compare) [with _RAIter = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = greater<int>]'
 4805 |       std::__sort(__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
      |       ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:18:11:   required from here
   18 |         std::sort(std::begin(data), std::end(data), std::greater<int>());
      |         ~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h:240:30: error: no match for call to '(std::greater<int>) (std::tuple<int, int, int>&, std::tuple<int, int, int>&)'
  240 |         { return bool(_M_comp(__val, *__it)); }
      |                       ~~~~~~~^~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_function.h:394:7: note: candidate: 'constexpr bool std::greater<_Tp>::operator()(const _Tp&, const _Tp&) const [with _Tp = int]'
  394 |       operator()(const _Tp& __x, const _Tp& __y) const
      |       ^~~~~~~~
/usr/include/c++/14/bits/stl_function.h:394:29: note:   no known conversion for argument 1 from 'std::tuple<int, int, int>' to 'const int&'
  394 |       operator()(const _Tp& __x, const _Tp& __y) const
      |                  ~~~~~~~~~~~^~~
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Iter_comp_val<_Compare>::operator()(_Iterator, _Value&) [with _Iterator = __gnu_cxx::__normal_iterator<std::tuple<int, int, int>*, std::vector<std::tuple<int, int, int> > >; _Value = std::tuple<int, int, int>; _Compare = std::greater<int>]':
/usr/include/c++/14/bits/stl_heap.h:140:48:   required from 'void std::__push_heap(_RandomAccessIterator, _Distance, _Distance, _Tp, _Compare&) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Distance = long int; _Tp = tuple<int, int, int>; _Compare = __gnu_cxx::__ops::_Iter_comp_val<greater<int> >]'
  140 |       while (__holeIndex > __topIndex && __comp(__first + __parent, __value))
      |                                          ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:247:23:   required from 'void std::__adjust_heap(_RandomAccessIterator, _Distance, _Distance, _Tp, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Distance = long int; _Tp = tuple<int, int, int>; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
  247 |       std::__push_heap(__first, __holeIndex, __topIndex,
      |       ~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  248 |                        _GLIBCXX_MOVE(__value), __cmp);
      |                        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_heap.h:356:22:   required from 'void std::__make_heap(_RandomAccessIterator, _RandomAccessIterator, _Compare&) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
  356 |           std::__adjust_heap(__first, __parent, __len, _GLIBCXX_MOVE(__value),
      |           ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  357 |                              __comp);
      |                              ~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1593:23:   required from 'void std::__heap_select(_RandomAccessIterator, _RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1593 |       std::__make_heap(__first, __middle, __comp);
      |       ~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:1868:25:   required from 'void std::__partial_sort(_RandomAccessIterator, _RandomAccessIterator, _RandomAccessIterator, _Compare) [with _RandomAccessIterator = __gnu_cxx::__normal_iterator<tuple<int, int, int>*, vector<tuple<int, int, int> > >; _Compare = __gnu_cxx::__ops::_Iter_comp_iter<greater<int> >]'
 1868 |       std::__heap_select(__first, __middle, __last, __comp);
      |       ~~