數學專題

M1 最佳兵力募集模型

此研究總體目標為找到一個台灣最佳募兵方案。用給付月薪及服役時間定義一位士兵的品質；依據給付的月薪、日常開銷和社會成本三項計算訓練一個士兵的成本；假設國防薪水預算為定值，列出預算與義務役和志願役的月薪、人數及工作時間的關係。整合上述為兵力募集總效用函數，考慮貢獻品質時間的不同，建立三個不同的數學模型。比對三種數學模型，並基於得到的結果，給予政府募兵策略的建議。

M2 Cross Out the Lights──Lights Out Variations

In the original Lights Out Game, pressing any of the lights will toggle it and the adjacent lights, and the goal of the game is to switch all the lights off. In this study, we designed the variations of Lights Out Game, including the “Rook Cross Rule” and the “Bishop Cross Rule”. We investigated the necessary condition and the solution in the solvable configurations, and further discussed the similarity between the rules.

M3 Elimination Game-Discuss the Minimum of Must-pass Storage Spaces

We were inspired by the game “Sheep n Sheep”. We can eliminate all the cards in any order of the cards we click on. We simplify the problem and figure it out by using Pigeonhole principle and finding the cycles. Eventually, we find the general formula of the minimum of must-pass storage spaces in the case of k elimination, two or three types of cards, n sets in every type of cards, and two layers

M4 Face to Face - Study of the Rolling Plato Polyhedrons on Tessellations Problem

In our research, we study the rolling tetrahedron, hexahedron, octahedron and icosahedron problems.

M5 Magic Poker ──撲克牌魔術揭密

在本篇研究中，我討論了不同張數、堆數下，藉由不斷選出目標牌，然後將它依規定疊合後重新發牌，試著找出規律其中規律。我發現在奇數堆的狀況下，奇數張牌時目標牌會藉由洗牌收攏回目標位置，而偶數張牌時則會循環，而偶數堆的狀況下，3的倍數張牌時，目標牌會循環，而牌數非3的倍數張時，藉由洗牌能收攏回目標位置。未來想研究目標牌在不同情況下，移動至目標位置的最少步數與n、k之間的關係。

M6 橫看成嶺側成峰－摩天大樓數獨之探討

摩天大樓數獨是一款花式數獨，表格內的數字代表大樓高度，而表格外的提示數代表從該方向可看到的大樓數量。本研究分別討論一維與二維表格，以及討論特定狀況的條件與計算符合的排列數量。

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