• Fill the circles with the numbers 1 to 9 such that each side of the triangle totals 17?

Start off your summer, June 20, 5:09 pm PDT, with a dash of brain lubrication. I remind myself that these oldie-but-goodie chestnuts are new to every generation. Like jokes, their origination is lost in the mists of time.

1. In your basement are three unmarked light switches, all of them currently in the OFF position. Each switch controls one of three different tungsten lamps on the floor above. How can you determine which switch goes to which lamp with just one trip upstairs? (Look for the "aha" clue!)

2. Three hats marked "black-black," "white-white," and "black-white" originally contained two black balls, two white balls, and one of each, but someone switched the labels so each hat is now incorrectly labeled. Without looking into the hats, you can take out one ball at a time. How many drawings do you need to figure out the contents of each hat?

3. You've got a 5-gallon pail, a 3-gallon pail, and unlimited water. How can you put four gallons of water in the 5-gallon bucket?

(Assume for the next two puzzles that every birth has a 50/50 chance of being either a boy or a girl.)

4. Q: How many children do you have? A: Two. Q: Is one of them a girl? A: Yes.

What is the probability that the other child is a girl?

5. Q: How many children do you have? A: Two. Q: Is the older one a girl? A: Yes.

What is the probability that the other child is a girl?

Barry Evans (barryevans9@yahoo.com) is still trying to puzzle his way out of the Box of Life.

CAPTION: 

[PLEASE PRINT ANSWERS UPSIDE DOWN IN A SMALLER FONT]

1: Turn one switch on and leave it on for two minutes. Turn it off. Turn a second switch on and run upstairs. The warm bulb of one of the two "off" lamps corresponds to the first switch. And, of course, the "on" lamp corresponds to the switch you left on. (I specified "tungsten" because it stays warm, unlike CFLs.)

2: One. Pick a ball out of the B-W hat. If it's white, then this hat contains two white balls (it can't contain one each black and white, since it's incorrectly labeled). So the hat labeled W-W must contain two black balls, and the hat labeled B-B contains one of each. Vice versa if you draw a black ball.

3: Fill the 5-gallon pail and pour it into the 3-gallon pail, leaving 2 gallons in the 5-gallon pail. Empty the 3-gallon pail and pour the 2 gallons from the other pail into it. Fill the 5-gallon pail again and use it to top up the 3-gallon pail, leaving 4 gallons. More prosaically, 4 = 5 - [3 - (5 - 3)]

4: 1 in 3. The possibilities are older girl-younger girl, older girl-younger boy, older boy-younger girl, older boy-younger boy (GG-GB-BG-BB). The second answer eliminates BB, leaving three possibilities, only one of which is GG.

5: 1 in 2. Of the four possibilities GG-GB-BG-BB, #3 and #4 are eliminated by the answer to the second question, leaving two possibilities, only one of which is GG. Interesting, isn't it, that knowing the birth order changes the odds?

Diagram: Starting at a vertex, one solution is 1-5-9-2-4-8-3-6-7. (The sum of the digits 1 to 9 is 45; and the sum of the digits on each of the three sides is 3 x 17 = 51, with each vertex being counted twice. So the sum of the vertexes is 51 - 45 = 6, giving 1-2-3 for the vertexes - then it's easy.)