Well done to Alex Labram, age 16, of Waingels Copse School, Reading, who cracked this Tough Nut. He ended up checking through every combination of the numbers and operations until he found the one that worked, using a spreadsheet to save a bit of time.

Before Alex found the solution above, lots of people tried bending the rules:

Callum Gilmour (S3, Madras College, St Andrew's, Scotland) and Bei Guo (14, Riccarton High School, Christchurch, New Zealand) both noticed that the problem can be done with a square root sign:

David White (age 17, Alcester Grammar School) added in factorial notation:

Ben Falconer (S2, Madras College) used a bit of rotation:

8 ×3 +  3 ∞

Sarah Dunn (S2, Madras College) decided that working in another base might help. Since there is an 8 in the problem, she decided to try base 9, and came up with:

Tim Whitmore (S6, Madras College) used recurring decimals:

Finally, Ravi Raja, (age 20, St Xavier's College, Calcutta) used the greatest integer function, [x].
[x] is the greatest integer which is less than or equal to x.