Puzzles
Using exactly four 4s, can you make every whole number from 0 to 10?
Using exactly four 4s each time, plus any of +, −, ×, ÷, √, !, decimal points and parentheses, form an expression equal to every whole number from 0 to 10. (4 ÷ 4 + 4 ÷ 4 = 2 gets you started.)
Reveal the answer
All of them work: 0 = 4−4+4−4, 1 = 4÷4+4−4, 2 = 4÷4+4÷4, 3 = (4+4+4)÷4, 4 = 4+4×(4−4), 5 = (4×4+4)÷4, 6 = (4+4)÷4+4, 7 = 4+4−4÷4, 8 = 4+4+4−4, 9 = 4+4+4÷4, 10 = 4÷.4+4−4. First printed in 1881 in the magazine Knowledge, the puzzle gets far harder past 20 — numbers like 113, 157 and 347 are notoriously difficult to reach with only four 4s under the standard rules.