Use exactly four 7s to make 100
Professor Rackbrane's classroom challenge: using exactly four 7s and any ordinary arithmetic signs (plus, minus, times, divide, decimal points, brackets), write an expression that equals exactly 100. No other digits are allowed, and you must use all four 7s — no more, no fewer.
Reveal the answer
(7 ÷ .7) × (7 ÷ .7) = 10 × 10 = 100 — dividing 7 by the decimal .7 (seven tenths) gives 10, so squaring that gives exactly 100. Henry Dudeney set this as puzzle no. 95, 'The Four Sevens,' in Amusements in Mathematics (1917); the same trick works for any digit substituted for 7.
— Henry Ernest Dudeney, Amusements in Mathematics — 1917, puzzle no. 95
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