Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
Can you explain the strategy for winning this game with any target?
We received several responses mentioning that a strategy of trial and error had been used to arrive at the result. This is a valuable strategy but it may be difficult to tell if there is more than one solution.
Zak and Sam from Norwich School for boys showed that this solution works:
Ian from Myton School reasoned as follows:
Ben's approach confirmed that there is a single solution:
$E$ is a multiple of $5$, $B$ of $3$ and $J$ of $4$.
A student from Carres Grammar School used simultaneous equations to arrive at the solution:
Knowing that $x$ is a multiple of $3$, $y$ is a multiple of $4$ and $z$ is a multiple of $5$ then leads to the solution.
Well done to you all.