This is an extended version of previous Cross-Number Puzzles published here and here.

This time, the aim is to insert sixteen distinct 3-digit numbers into the grid such that every number is either a perfect square or cube.

Every number must be greater than 99, so there are no leading zeros. Numbers are read either left-to-right or top-to-bottom. The larger outer cross requires twelve numbers and the inner cross has space for four numbers; the circle in the centre will have a digit that is the first digit of two numbers and the last digit of two other numbers.

I have found one solution, but there may be more.

When submitting your answers, just write out a chain of numbers going clockwise round the outer cross, for example, starting at the top, 441 – 125 – 529 – 961 – 361... and so on. Then write the four numbers in the centre cross.

Have fun!

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**How to Enter****Send your complete solution by email to pmq22pearson@giftedmaths.com.**This email address shall be removed after the competition closes to avoid spam.

**This PMQ22 competition closes on MONDAY 10 June at 23:59 GMT - one extra weekday from now on**.

**The Prize****The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR.**The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

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Enjoy the challenge!

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