Sunday Times Teaser 2746 – Five Finger Exercise
by Danny Roth
Published: 10 May 2015 (link)
George and Martha have a five-figure code for their burglar alarm. George commented that the three-figure number formed by the first three digits of the code equalled the sum of the cubes of those first three digits. Martha added that the three-figure number formed by the last three digits of the code equalled the sum of the factorials of those three digits. (She had to remind George what a factorial was — he remembered once she had pointed out that the factorial of 4 was 4x3x2x1 = 24.)
What is their code?