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What is the digit $x$ in this cross-number?

Across Down

1. A cube 1. One less than a cube

3. A cube 2. A number

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

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

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This problem is taken from the UKMT Mathematical Challenges.