### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Have You Got It?

Can you explain the strategy for winning this game with any target?

### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Change the order of the fractions in the sum so that fractions whose denominators share more factors are added first: \begin{align}&\tfrac{1}{7}+\tfrac{1}{8}+\tfrac{1}{9}+\tfrac{1}{10}+\tfrac{1}{11}+\tfrac{1}{12}+\tfrac{1}{14}+\tfrac{1}{15}+\tfrac{1}{18}+\tfrac{1}{22}+\tfrac{1}{24}+\tfrac{1}{28}+\tfrac{1}{33}\\ &=\hspace{2mm}\tfrac{1}{7}\hspace{1mm}+\tfrac{1}{14}+\tfrac{1}{28}\hspace{2.5mm}+\hspace{3.5mm}\tfrac{1}{8}\hspace{1mm}+\tfrac{1}{12}+\tfrac{1}{24}\hspace{2.5mm}+\hspace{4.5mm}\tfrac{1}{9}\hspace{1mm}+\tfrac{1}{18}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{1}{10}+\tfrac{1}{15}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{1}{11}+\tfrac{1}{22}+\tfrac{1}{33}\\ &=\hspace{1.7mm}\tfrac{4}{28}+\tfrac{2}{28}+\tfrac{1}{28}\hspace{2.2mm}+\hspace{2.5mm}\tfrac{3}{24}+\tfrac{2}{24}+\tfrac{1}{24}\hspace{2.5mm}+\hspace{3.1mm}\tfrac{2}{18}+\tfrac{1}{18}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{3}{30}+\tfrac{2}{30}\hspace{2.5mm}+\hspace{2.5mm}\tfrac{6}{66}+\tfrac{3}{66}+\tfrac{2}{66}\\ &=\hspace{13.2mm}\tfrac{7}{28}\hspace{14mm}+\hspace{14.25mm}\tfrac{6}{24}\hspace{14.25mm}+\hspace{8.5mm}\tfrac{3}{18}\hspace{9mm}+\hspace{8.5mm}\tfrac{5}{30}\hspace{8.5mm}+\hspace{13mm}\tfrac{11}{66}\\ &=\hspace{14.3mm}\tfrac{1}{4}\hspace{14.4mm}+\hspace{15.3mm}\tfrac{1}{4}\hspace{15.3mm}+\hspace{9.4mm}\tfrac{1}{6}\hspace{9.3mm}+\hspace{10.3mm}\tfrac{1}{6}\hspace{9.4mm}+\hspace{13.3mm}\tfrac{1}{6}\\ &=\hspace{3mm}1\end{align}