You are given two sequences of positive integers which do include the numbers from 1 to 15 (1 and 15 inclusive) and 1 and 18 (1 and 18 inclusive).

For each of these sequences you are asked to make alternating additions and subtractions using the numbers belonging to a sequence such that you use all the numbers in valid mathematical equations just once and you eliminate all the numbers , ie there is no number which remains unused in an equation.

Is it possible to obtain the objective for both sequences ?

For an example of how the game would go suppose you start with the sequence of numbers from 1 to 15. Starting from it you use addition once using 3 numbers from the sequence by adding 2 of them which result in the 3nd number.

This is followed by subtraction which applies the same method until , if possible you eliminate all numbers.

Also , for clarification the 2 sequences are independent of one another.

You receive the sequence 1 to 15 and the one of 1 to 18 and applying operations to one doesn't affect the other.

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