DAY 426

LOOSE CHANGE
Credit: GAMES Magazine
July, 1983
Jerry Weinberg

You probably collect a handful of change (pennies, nickels, dimes, and quarters) every day. Which coin, on average, will you receive the least of - and why?

Answer:

Nickels ............. Suppose that 99 people go into a store, one after another, and purchase items costing 1 cent, 2 cents, 3 cents .......... through 99 cents, giving the storekeeper a $1 bill in each case. Assuming the storekeeper has sufficient pennies, nickels, dimes, and quarters, and distributes them in the standard manner (a dime instead of two nickels, etc.), the change will break down thus: 200 pennies, 40 nickels, 80 dimes, and 150 quarters. 

If you still have doubts, try holding your change aside for a week or two, and see for yourself.

DAY 425

PASS THE SOAP
Credit: GAMES Magazine - Mar. 1983
Clara Hall

The cold-water tap fills our tub in 6 minutes 40 seconds, the hot water tap in 8 minutes. The tub drains in 13 minutes 20 seconds. If the stopper is out and the taps run full force, how long will it take the tub to fill? (And how much water will be wasted?)

Answer:

The tub will fill in 5 minutes........The cold faucet fills the tub in 400 seconds (1/400 per second), the hot faucet in 480 seconds (1/480 per second). The tub empties 1/800 of its contents per second. So with both faucets and the drain working together, 1/400 + 1/480 - 1/800, or 1/300 of the tub, gets filled each second. Therefore, the tub will be filled in 300 seconds, or five minutes. Since 1/800 of a full tub empties each second, the amount of water wasted  is 1/800 of a second X 300 seconds = 3/8 of a full tub.