In the 1982 SAT, only 3 of 300,000 students answered a circle rotation problem correctly. Even the test makers were wrong, and the correct answer was not among the choices. The key is the coin rotation paradox: a circle rolling around an equal circle makes 2 full turns, not 1.
The "Rule of 72" lets you quickly estimate compound interest. Divide 72 by the interest rate to find how many years it takes to double your money. At 6% annual return, 72 ÷ 6 ≈ 12 years to double. The actual result is 2.012×—remarkably accurate.
There's a quick way to estimate square roots. Find the nearest perfect square, take its root, then add the difference divided by twice that root. For √17: √16 = 4, plus (17−16)÷(4×2) = 0.125, giving 4.125. The actual value is 4.123—almost exact.