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Adjacent Additions

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

In a $7$-digit numerical code each group of four adjacent digits adds to $16$ and each group of five adjacent digits adds to $19$. What is the sum of all seven digits?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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