Recently I baked a spherical cake (3cm radius) and invited over a few friends, 6 of them, for dinner. When done with main course, I thought of serving this spherical cake and to avoid uninvited disagreements over the size of the shares, I took my egg slicer with equally spaced wedges(and designed to cut 6 […]

The tradition way for two children to divide a piece of cake fairly between them is “you cut, I choose”, What process accomplishes this is intuitively clear. Is there a similar process which works for $3$ children. Suppose that three children $(1),(2)$ and $(3)$ have associated measures (ways of evaluating the pieces of cake) $\alpha_{1},\alpha_{2}$ […]

When flipping a coin to make important decisions in life you can flip once to choose between 2 possible outcomes. (Heads I eat cake, Tails I eat chocolate!) You can also flip twice to choose between 4 outcomes. (Heads-Heads, Tails-Tails, Heads-Tails, Tails-Heads) Can you use a coin to choose evenly between three possible choices? If […]

Recently I baked a spherical cake ($3$ cm radius) and invited over a few friends, $6$ of them, for dinner. When done with main course, I thought of serving this spherical cake and to avoid uninvited disagreements over the size of the shares, I took my egg slicer with parallel wedges(and designed to cut $6$ […]

This is a problem that has haunted me for more than a decade. Not all the time – but from time to time, and always on windy or rainy days, it suddenly reappears in my mind, stares at me for half an hour to an hour, and then just grins at me, and whispers whole […]

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