examday

/TMUA

You and your friend are playing a game of distributing weights. Each of you has a bag containing a certain real, discrete amount of weight (unit: kg). Let $x$ represent the weight in your bag, and $y$ represent the weight in your friend's bag. You want to adjust the weights in your bags such that $x-y$ is minimised, while satisfying the following conditions:

• 1. Your friend must have at least 1 kg in their bag.
• 2. The weights of your friend cannot exceed twice the weights of yours minus 1.
• 3. The total weight in both bags cannot exceed an unknown value $m$.

After calculating, you find that the minimum value of the difference between your weight and your friend's is $-1$, i.e. $x-y=-1$. Now, you need to find the maximum allowed total value $m$ that satisfies these conditions.