Henry Ernest Dudeney/Puzzles and Curious Problems/118 - Six Simple Questions/Solution

by : $118$

 * Six Simple Questions

Solution
The answers given by to these trick questions are as follows:


 * $(1): \quad 8111 \tfrac 1 2$


 * $(2): \quad 18 \tfrac 2 3$


 * $(3): \quad 1$ and $7$


 * $(4): \quad 1 \tfrac 1 5$


 * $(5): \quad 8 \tfrac 1 4$


 * $(6): \quad \tfrac 6 9$

but these are not necessarily the only solutions.

Proof

 * $(2): \quad$ Trick question.
 * There is a case for exploiting another trick: adding $3$ to $182$ and inserting a decimal point to make $18 \cdotp 5$.


 * $(3): \quad 7$ is of course prime.


 * $(4): \quad$ It does not say how those $3$ figures are to be combined.


 * $(5): \quad$ If $5 \times 4 = 33$, then $20$ is identified with $33$.
 * Hence dividing $20$ by $4$ is dividing $33$ by $4$, which is $\tfrac {33} 4 = 8 \tfrac 1 4$.
 * Messy and unsatisfying question, as the initial concept is absurd and meaningless.


 * $(6): \quad$ By "reversed", means "turned upside down".
 * But there is an argument for "reversed" meaning "reflected in the vertical axis", in which case $\tfrac 1 8$ does the job just as well.