Volume 3

1966

In 1782 the Swiss mathematician, Leonard Euler, perhaps the greatest mathematician of the eighteenth century, published a paper bearing the title "On a New Type of Magic Square".

J71 Find a four digit number which on division by $149$ leaves a remainder of $17$ and on division by $148$ leaves a remainder of $29$.

J61 A strip of pasture land is divided into three paddocks whose areas are 35 acreas, 10 acres and 65 acres.

Let $a,b,c,d,e,f$ represent the integers $1$ to $6$ in some order. If $a+b < c+d$ and $c+e<a<f$, identify the values of the six integers and prove that the solution is unique.