解題小工具 - 輕鬆解答數學比賽最新題目 / A simple tool to tackle the latest math competition

每一次我也相當期待 @kenchung 的數學比賽，因為我喜歡用不同的方法解答問題。可是我的程式語言並不好，寫短短的語言可能要花大半天時間，有一些人也可能因此沒有參加這比賽。這是非常可惜的。這一次的題目是要從十多個的方程式去把未知數尋找出來。?簡單的方法是把所有的方程式寫出來，然後把他們加加減減，把逐一個未知數找出來。第二個方法是用程式暴力解題。我看了題目便認為有可能用 Excel 的 Add-in (Solver)，直接把所有條件輸入，把所有回答一次過找出來。 也順便分享此方法給大家，以後也有可能用同樣的方法參加比賽。

I always have high expectation to @kenchung maths competition because I always like to use different ways to solve the question. However, my programming skill is not very good and a short code can cost me plenty of time. That may be also the reason why not more people join the competition and this is a real pity. For this competition, we are required to solve the unknown variables by using 10+ conditions. There are few ways to solve that: 1) write down all the formula and use simple algorithm to find out the variables one by one. 2) Use brute force to calculate the answer programmatically. I also thought there are the third way and a way everyone can do it easily: By using the built in tool within excel (solver) to calculate all the variable at once. I will share the method to everyone such that I hope it will encourage more people to participate the competition in the future.

第一步是在 Excel在特訂的範圍內輸入 1-16 ，這範圍是會讓 Excel 進行計算的。

The first step is to input 1-16 into a range within Excel, the range will be used to calculate the answer later.

第二步是在 Excel 內把所有的條件列出來（藍色），紅色部分是使用來有核對答案的。

The second step is to list all the conditions (blue), the red part is to validate the answer later on.

第三步是打開 Solver 的功能，再把藍色的條件輸入到"設定限制式裡面"， 其中還會要求結果是不能重複和必須是整數。

The third step is to open the solver function and input the conditions (blue) into the excel, in particular I will add two more conditions (to ensure the result do not duplicate and must be integer).

可是用這些條件，Excel 並未能把回答算出，原因是首四個條件 "A, B, J, K 只可由 2, 4, 6, 8 四個數字填上" 對於 Solver 來說太複雜，所以我會在 Solver 把這四個條件移除，然後再執行一次。

Unfortunately Excel could not give me the answer in the first go because the condition of "A, B, J, K can only be filled with the numbers 2, 4, 6 or 8" is too complex for Excel and therefore I will remove these conditions and re-run the program.

最後Excel把回答算出來了，只有一個條件沒有達成，我們可以很簡單把 J 和 H 的位置互換，便是這次比賽的答案。

Finally, after the changes, Excel is able to calculate the answer for me but with one condition not being fulfilled. We can simply switch the output for J and H and we have our answer for this competition.

希望下次你們也可以一起參加～

Hope you enjoy it and hope to see you in the next competition.