A number trick: think of a number, add 5, double it, subtract 10, then halve it — you get back the…

Why

Disha's caution is exactly the right instinct in general — one successful test with one number is never proof that something ALWAYS works, and questioning a pattern after seeing it hold just once is good habit, not doubt for its own sake. In this particular case, though, the trick can be checked with a letter standing for ANY number, not just 7, and that check settles it completely. Call the starting number x: add 5 gives x+5; double it gives 2x+10; subtract 10 gives 2x; halve it gives x — back to exactly where it started, and notice that the +5 and −10 (which became −10 after doubling) cancelled out through the algebra regardless of what x actually was. Because the letter x could stand for any number at all during that working, the result holds for every number, not just the one tested. Test: try the same steps with a different starting number, say 20 — add 5 (25), double (50), subtract 10 (40), halve (20) — back to 20 again, exactly as the algebra predicted. No, it works for every number: using a letter to stand for 'any number' and following the steps algebraically proves the trick for all numbers at once, which is a stronger kind of proof than testing one example.