Swapping the Roles

Here is a trick that works great in coaching - whether for a math test, spelling test or almost anything else.  Ask your kid to be the teacher and give you the exercises that she/he think are going to be on the test. The hardest ones. While you will be playing a role of a student that solves the test but makes some mistakes. Let your kid check your test and find these mistakes.  Also, let her/him grade you.  Spice it up by playing misbehaving kids, excelling kids, failing kids. This is usually much more fun for them than the regular way of test prep.

I tried this with my daughter this week in preparation for her multiplication test. 20 multiplication exercises. I could solve only half... She liked it so much that next day she prepared a test sheet for me in advance at school and an answer sheet for her to grade me.

Now, let's try doing something similar with our puzzle today. Here is the story. Find what's wrong with it.

You want to send your kids to an 8-week long sleep away summer camp. But you don't have the $1,997 that it costs. How about asking for help from the grandparents? Each couple offers to give $1,000 toward the camp. You get the $2,000, pay for the camp and receive a $3 change. As a gesture you want to give each of the set of grandparents a $1 of change, and you keep a $1 for yourself as $3 is not divisible by 2.  So, now you owe each couple of grandparents $999, together you owe them $1,998. And you have $1 in your hands.  As you started with $2,000, this means that $1 + $1,998 = $2,000.  Right?

Disclosure: this puzzle is reinterpretation of a famous missing dollar puzzle that we discussed long time ago.

Dollar image from Flickr, distributed under CCL. Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Average Bunk Size

You are checking out an overnight camp for your kids for next year. On your family visit to the camp you ask 30 randomly encountered kids what is their bunk size and record all the answers. Surprisingly, the answers deviate quite a lot. How can you figure out (approximate) average bunk size from all these numbers?

Image by New York YMCA camp, distributed under CCL.

This is a tricky puzzle and therefore I am giving one whole week for contemplation and answer submission. At the present moment I don't know either how this should be solved but I do know how this should not be solved. So, let's figure it out together. Answer ideas accepted any time until next Friday July 22nd, on our Family Puzzle Marathon. They will be hidden till then and everyone who suggested something reasonable will get a puzzle point.

Packing for a sleep-away camp

Remember the old-fashioned bars of soap? You are trying to figure out whether one would be enough to give to your son for four weeks of the sleep-away summer camp. I know, most of them never wash there, but let's hope that this time he will. You notice that when you leave this soap in the kids' bathroom and check in a week, all of its dimensions seem to erode by two: it has only half of the original height, half of the original width, and half of the original depth. But at home both of your kids are using it, in the camp it will be only for your son. How can you figure whether to pack one or two bars?
(this puzzle is adapted from a book by C. Koval)

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Camp Dilemma

Here, on the North East of the US we have a winter school-break that many use to escape to warmer places. Or, on the opposite, to live the winter to the fullest, and go skiing, tubing or skating. For those of us who finished all the vacation days during the Holiday break, there is TV babysitting or kids' vacation camps. A week of vacation camp costs $250, if you pay on or before the first day of the camp. If you choose to go and pay day-by-day, it is $60 per day. Can you help me figure out whether to sign my daughter for the whole week or on a day-by-day basis? Our past camp experience shows that she will definitely enjoy four days, but she frequently gets tired and refuses to go on the fifth. Let's say that we are only 50% certain that she will stay for 5 days.

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Field Trip Permission Form

Mt Ida day summer camp is having a field trip next week. In order to go on a trip each out of 400 campers should bring a field trip permission form home and return it back with a parents' signature. From the past camp experience, only about 90% of the forms sent are reaching parents, getting signed and returned back on the next day. The rest of the forms are disappearing somewhere in the backpacks alongside wet swim suits, gimp and snack crumbs. The question is, when should camp management start sending home the permission slips, so that in a week they would have all the forms back.
Note: floating point numbers could be rounded.

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

One hectic summer morning

Summer is not easy on the working parents. Camps are usually further away from home than schools are, camps start later and end earlier than schools. So, go figure how to squeeze an 8-hour working day in-between...

Here is a puzzle inspired by my friend's real life story.
She lives 15 miles South from where she works.
Her son goes to a camp 10 miles West from home. She drops him off, then heads to work. As she is not able to pick her son from the camp at 4pm, she arranged a carpool with another family, that unfortunately lives in the opposite direction: 5 miles East from her. So, on a regular camp morning, my friend leaves her house early to pick up this other kid, then drives both kids to the camp and then continues to work. In addition to all this, on one morning last week she got a call from a friend from work. Friend had some car trouble and pleaded to be picked up on her way to work. Friend lives 2 miles South from my friend's home.
What is the minimum number of miles my friend had to travel on this hectic morning before reaching her work?



Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Summer Camp Lunch Dilemma

Here is my real life puzzle:
My daughter goes to a summer camp where I can either send her a lunch from home or order lunch from the cafeteria for $5. Cafeteria offers a number of lunch selections, but what my daughter likes is:
8oz mac-and-cheese with 5 grape tomatoes
or
bagel with cream cheese and 5 baby carrots

Ordering lunch from the cafeteria has a number of advantages: less work for me in the morning, lighter camp backpack for my daughter, food is presumably fresher than when made in the morning at home. However, it is an additional $25 per week.
How much could I save in a week by preparing identical lunches for my daughter at home?

How many campers in a bunk?

Open day in a summer camp. A prospective family comes in, observes camp pictures and asks "How many campers do you have in a bunk? Around 100?"
"No, far away from a 100" - answers the camp director.
"If we would double the amount of kids in one bunk, add to it half of the amount of kids in a bunk, and then add another quarter of the amount of kids in a bunk, and then add your son, then we would have a 100."
How many kids are there in a bunk?

Popsicle sticks

You have gathered 22 Popsicle sticks. How can you use them to mark a rectangle of the largest area, without breaking the sticks?

Lice Alert

Have you had a wave of head lice going through your child's school, camp or day care? Frustrating and tedious daily combing, nurse calls, parent whisper, days off from school, infinite laundry, empty shampoo shelves at the pharmacy, angry haircuts - all these efforts devoted to fighting a ferocious tiny insect.
How quickly do you think head lice could spread around if we do nothing?
Let's pretend that each day lice spreads from one child to three more. And that lice is smart and populates only "virgin" territories avoiding already infested heads. Say, there are 400 kids at school. And it all starts with a single nit in one child's hair.
How many days would it take for everyone at school to get infested?

P.S. No, we have not had any lice in our neighborhood in the past two years, but swine flu panic was a reminder.