Puzzles

This year, I have spend a lot of time working on the AVE game engine. Today's answer is the code to the safe in this Christmas themed game.

The smallest number that is equal to the sum of its digits multiplied by ten more than the sum of its digits.

You start at A and are allowed to move either to the right or upwards.

How many different routes are there to get from A to B?

Today's number is the second smallest number that can be written as a×b×c×d×e×f×g×h×i, where a,b,...,i are all integers greater than 1.

Put the digits 1 to 9 (using each digit once) in the boxes so that the three digit numbers formed (reading left to right and top to bottom) have the desired properties written by their rows and columns.

When you add up the digits of a number, the result is called the digital sum.

How many different digital sums do the numbers from 1 to 10⁹¹ have?*

Today's number is the number of ways that 35 can be written as the sum of distinct numbers, with none of the numbers in the sum being divisible by 9.

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the product of the digits in the red boxes.