Think of a Number/Examples

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Examples of Think of a Number puzzles

Rhind Papyrus Problem $28$

$\dfrac 2 3$ is to be added.
$\dfrac 1 3$ is to be subtracted.
There remains $10$.

Rhind Papyrus Problem $30$

If the scribe says to thee:
$10$ has become $\dfrac 2 3 + \dfrac 1 {10}$ of what?

Rhind Papyrus Problem $33$

A number, plus its two-thirds, and plus its half, plus its seventh, makes $37$. What is the number?

It is to be expressed in Egyptian form.

Bachet: $1$

A person chooses secretly a number, and trebles it, telling you whether the product is odd or even.
If it is even, he takes half of it,
or if it is odd, he adds one and then takes one half.
Next he multiplies the result by $3$,
and tells you how many times $9$ will divide into the answer, ignoring the remainder.
The number he chose is -- what?

Bachet: $2$

The subject chooses a number less than $60$
and tells you the remainders when it is divided by $3$, $4$ and $5$, separately, not successively.
The original number is -- what?

Bachet: $3$

The first person takes a number of counters greater than $5$.
The second person takes $3$ times as many.
The first person gives $5$ counters to the second.
The second person then gives the first $3$ times as many as the first person holds in his hand.
How many counters has the second person got in his hand?