9 + 10 + 11 + 12 = 13 + 14 + 15
Science & Math
Good Advice
“There are two rules for success,” says Raymond Smullyan. “Rule number one: Never tell all you know.”
Oops
Math Notes
Double Duty
A “multi-magic” square: Each row and column sums to 260; square each term and they sum to 11,180.
Half Right
“Numero deus impare gaudet [the god delights in odd numbers].” — Virgil
“Why is it that we entertain the belief that for every purpose odd numbers are the most effectual?” — Pliny
“This is the third time; I hope good luck lies in odd numbers. … They say there is divinity in odd numbers, either in nativity, chance, or death.” — Shakespeare, The Merry Wives of Windsor
Simple Enough
Before his students arrived for a graduate course in logic, Raymond Smullyan wrote on the blackboard:
PLEASE DO NOT ERASE — BECAUSE IF YOU DO, THOSE WHO COME LATER WON’T KNOW THAT THEY SHOULDN’T ERASE.
Math Notes
Galton’s Paradox
Suppose you flip three fair coins.
Necessarily two will match, and it’s an even chance whether the third will be head or tail.
Therefore the chance that all three will match is 1/2.
Math Notes
8589934592 × 116415321826934814453125 = 1000000000000000000000000000000000