Let's denote the sizes of the cloaks and crowns as follows:
- Prince cloak size = P
- King cloak size = K
- Emperor cloak size = E
- Prince crown size = p
- King crown size = k
- Emperor crown size = e
From the given information, we can deduce the following:
- Ahmose's cloak size is larger than Kamose's cloak size.
- Ahmose's crown size is smaller than Thutmose's crown size.
- Thutmose's cloak size and crown size are both larger than Kamose's.
- Thutmose's crown size matches Kamose's cloak size.
Let's use these deductions to solve for each son's sizes:
- From deduction 1, we know that Kamose's cloak size must be P since it is the smallest size available.
- From deduction 2, we know that Thutmose's crown size must be e since it is the largest size available and Ahmose's crown size is smaller than his.
- From deduction 3, we know that Thutmose's cloak size must be E since it is the largest size available and both his cloak and crown are larger than Kamose's.
- From deduction 4, we know that Kamose's cloak size is the same as Thutmose's crown size, which we just determined to be e.
Therefore, the sizes of the pharaoh's sons are:
- Kamose: cloak size = P, crown size = e
- Ahmose: cloak size = K, crown size = p
- Thutmose: cloak size = E, crown size = e



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