By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23....

If the numbers $1$ to $5$ are written out in words: one, two, three, four, five, then there are $3 + 3 + 5 + 4 +...

$2^{15} = 32768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$. What is the sum of the...

Starting in the top left corner of a $2 \times 2$ grid, and only being able to move to the right and down, there are exactly $6$...

The following iterative sequence is defined for the set of positive integers: $n \to n/2$ ($n$ is even) $n \to 3n + 1$ ($n$ is odd) Using...

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. 37107287533902102798797998220837590246510135740250 46376937677490009712648124896970078050417018260538 74324986199524741059474233309513058123726617309629 91942213363574161572522430563301811072406154908250 23067588207539346171171980310421047513778063246676 89261670696623633820136378418383684178734361726757 28112879812849979408065481931592621691275889832738 44274228917432520321923589422876796487670272189318 47451445736001306439091167216856844588711603153276 70386486105843025439939619828917593665686757934951 62176457141856560629502157223196586755079324193331 64906352462741904929101432445813822663347944758178...

The sequence of triangle numbers is generated by adding the natural numbers. So the $7$th triangle number would be $1 + 2 + 3 + 4 +...

In the $20 \times 20$ grid below, four numbers along a diagonal line have been marked in red. 08 02 22 97 38 15 00 40 00...