A Pacifier Puzzle

Why pacifiers are almost always magically fall nipple-side-up saving us from the need to wash them before sticking back into baby's mouth? Ok, sometimes we do suck them before giving it back to our treasures. That, by the way, is the healthiest wash of all according to the latest research.

Three of my daughter's not-so-favorite pacifiers on the carpet of (oh!) our hotel room. Her favorite pacifier unfortunately doesn't fall nipple-side-up and didn't participate in this staged experiment.
If this reminds you a buttered toast paradox - you are on the right way to the answer.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Kids Magic Trick

This came in a magic trick box that our daughter picked for her birthday.  Exhausted from all the Bar Mitzvah preparations for her older brother and her own demands for a Harry Potter birthday party, we didn't have any time to buy her a present or even think of anything original to serve as a present. As soon as she realized that no wrapped packages should be expected, she pragmatically proposed that on our next trip to a toy store she will pick something that she likes, I will wrap it and we all pretend it was a surprise.

She chose two sale boxes: one with a hundreds of hip-hop tattoos and another with magic tools. Among dice, fake nails and blood in the magic box there were these cards. 

Now, pay attention, because it starts to be complex. 

Our daughter, the magician, would ask you to think of a number between 1 and 63. Do not reveal this number!

Then, she will show you these cards, one-by-one.

After seeing each card you will say whether the number you picked is on this card or not.

And then, after these 6 yes-no answers, she will guess your number!

Let's try. 

I pick 23.

A-yes

B-yes

C-yes

D-no

E-yes

F-no

She magically guesses: 23!

How does she know?

Quite simple. The instructions on this magic set tell her to add up all the left corner numbers from the "yes" cards.

A+B+C+E

1+2+4+16=23

Unbelievable!

Try it yourself and think how this could possibly work. Two puzzle points for any lead here.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Lost Teeth Puzzle

Teeth is an important topic of discussion in our home. Our 12-year old son recently lost his tooth in ... a swimming pool. Our 9-year old daughter keeps counting her lost teeth, wiggly teeth and growing teeth.  Every few month she goes on an ice-cream diet because everything else just hurts too much when your wiggly tooth is hanging on a muscle thread. And our 1.5-years old finally got her first four teeth to cut and chew a grownup food but is drooling, sucking and crying while another one is growing.

My husband and I are doing pretty well with our teeth this year but this may very well be because our dentist died... and we haven't found a new one yet to tell us what is wrong with our teeth.

So, an easy puzzle for tooth owners of all ages.

My 10-year old daughter came to me telling that she was trying to count how many teeth she has lost overall.  But every time she counted she got a different number: 16, 17, 13, 15. She was asking what is the actual number of teeth she lost. Can you help her produce the best estimate from these numbers?

Image by Clintus McGintus, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

New House Puzzle

A man just finished painting his house and needs something more.
At the hardware store the clerk shows him what he wants and says, "one is $1."
"Fine," says the man, "I took 600, so here's $3."
What had he bought?

image by Padre MarianOne, distributed under CCL.

this nerve-wrecking puzzle is from The Mensa Genius Quiz Book but you don't need to be a genius to solve it. The House painting is a hint. Stand in front of your front house/apartment door and think what possibly can cost one for $1 and $3 for 600.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Number Tricks for You and Your Kids

The first one is for you:
How do you write 5 inside 4?
Hint: The Pope...


The second one is for your kids:
It is a hidden numbers game. Click below to view The Math Mom's logo. In it we hid at least 10 numbers. Print the image and together with your kids find all the numbers. Highlight them in a different color and email a snapshot to me.

Solve either trick and get one puzzle point. Solve both and get two. Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Why don't they flip?

You have seen them in DC, Philadelphia, Vancouver or other places around the world - cool sculptures that seem out of balance; sculptures that appear on the verge of falling yet are perfectly stable.
How is it possible?
I know this is not really math but semi-related.

HaBima square, Israel

Laguna Beach, CA, USA

Norway

England

Philadelphia, PA, USA

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

The Sleeping Mom Puzzle

As a mother of a 15-month old I have not slept straight through the night for weeks or months. Perhaps even years. My memory is so weakened by this lack of sleep that I don't even remember:)  February colds with caught and sneezes, belly ache, teething - all make their way to the sensitive mommy's ears waking me up a few times each night.  Every time I am awaken I barely remember who and where am I and whether this is the first time I am up this night or second.  So, here comes the puzzle:

You are going to sleep and you know that every night you will be awaken either once or twice, chances of each are equal.  Let's say a flip of a coin by a sleep angel decides: heads - you will be awaken once, tails - twice. You will be so tired that after waking up you will go back to sleep and you won't remember this awakening later on.  Now, I have two questions for you:

1. On any of these awakening, what do you think are the chances that the original coin showed heads?
2. Any time you wake up what are the chances that this is your first and only time awake this night?

This puzzle was invented by Arnold Zuboff and goes under a slightly different name which I will reveal later.

The sleeping mom and baby image by NoVa Hokie, distributed under CCL.

Your answers accepted any time until midnight on Sunday on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.