# The number circuit

The image circuit uses only positive integers. When a number enters this circuit it is placed in the Entry box and following the arrows it advances until it reaches the Exit. In each box you must perform the operation indicated and continue your journey.

If we arrive at the exit with the number 17. What number have we started with?

#### Solution

If it reaches the exit with 17, the last operation may have been to divide by 2 and in that case, we would have arrived at that box with 34, so we could not have arrived from the center (adding 37) nor multiplying by 6.

That is to say, that we arrive from another side to the exit, adding 8, so we have arrived at that box with a 9, and we can only arrive from the multiply by 3 box, which we will have reached with 3, from which a number is added its following.

The only way to reach 3 by adding a number to your next one is starting from 1, so that it has come out with 1, it has added 2 to the multiply by 3 box, it has gone to the box add 8 and it has arrived with 17.