Edition 0 | March 2015

SPARK

IGNITE YOUR MIND

© Qureeus Eduventures

WHAT IS SPARK?

A monthly newsletter that is your companion in the journey of thinking and discovery.

A selection of puzzles and exercises that you solve to conquer.And an article or two to enlighten you. To share with you the joy of

knowing.

Answers there are few, because the puzzles await to be solved by you.

WHO IS SPARK FOR?

Intended for students from Classes 6 to 10.But if you are inquisitive and enjoy exercising your mind, you should love

Spark!

HOW DO YOU GET YOUR SPARK?

Starting from April 2015, Spark comes to you.Subscribe today & join this journey of discovery, joy and growth.

Your school is a conducting a “Knockout Tennis Tournament”. Here, the moment someone loses, he or she is out of the tournament and the winner continues on.

61 students have signed up for the tournament. How many matches will be there until a Champion is crowned?

These aren’t questions & puzzles. Each is an opportunity to grow your mind and spark your neurons.

Try solving the question in whichever way you imagine:OnceTwiceThriceAs many times as necessary!

CLOCK IT

Remember that the fun & excitement is in the effort of discovering the answer - yourself! Not just reading it.

And don’t just keep your efforts to yourself. Share them with your parents, friends and us!

The best efforts shall be published in subsequent newsletters

How many times do the hour hand and minute hand of a clock come together (overlap) in24 hours?

(HINT: Try it with a real clock)

The mind is not a vessel to be filled, but a fire to be kindled“ -Plutarch

TACKLE THIS TOURNAMENT

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TACKLE THIS TOURNAMENT

A brilliant biologist genetically modified a bacterium that would split into two every minute and the population of bacteria would double.

He put one of his discovered bacterium in a petri dish. At the end of an hour, the petri dish was filled to the brim with bacteria. When was the petri dish half full?

BACTERIA ATTACK

My friend is a numismatist - a coin collector. On my birthday, he gifted me a set of 25 ancient and absolutely identical coins.

But the real gift is a puzzle! One of these coins is counterfeit (a replica of the original coins) and slightly heavier.

Can you help me find the counterfeit coin using just this pan balance? And in just three weighings?

THE COIN CONUNDRUM

How many matches would have been played if there were just 4 students?How about 10 students?

CLOCK IT

24? It’s not!Count it on a real clock with precise times or mark them on this clock.

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It’s not that I am so smart.It’s just that I stay with problems longer.“

-Albert Einstein

A thief and his friend (who is also a thief) get caught committing a theft. The police put them each in a different interrogation room and there is no way that the two thieves can communicate with one another.

The police realize that they do not have adequate evidence to put them in jail and if the thieves do not accept their crime, they will be able to walk away with only minor punishments.

The police decide to do something interesting. A deal is offered to each of the thieves - A & B.

If A says that B did the crime, while B does not accept, then A gets to walk away and B goes to jail for 5 years.

If A says that B did the crime AND B says that A did the crime, then both go to jail for 3 years each.

If A does not accept, but B says that he did the crime, then A will go to jail for 5 years while B will walk away.

TO DEFECT OR NOT TO DEFECT?

Remember:

Both A and B don’t know that they will be free if neither of them accept and they can’t communicate to each other in any way.

What should they do? Which option would you choose?

Let’s hear your thoughts!

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7 6 2

8 5

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7 1 9 2

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9

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1

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9 4

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4 2

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1 8

A Sudoku is a 9x9 grid as shown below. It is further divided into 3x3 sections.

Your task is to fill it with digits from 1 to 9 such that each digit appears just once in every column, every row and every 3x3 section.

Observe and start solving!

Let’s get you started:

Look at the top-left box.

Which numbers are missing? 1, 3 and 9.

If you observe the left-most column, it already has a 9 at the bottom.

So where can 9 go in the top left corner section?

SUDOKU - OBSERVE AND SOLVE

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BACTERIA ATTACK

The bacteria double in number each minute. If at x th minute, the petri-dish was half full, then at (x+1)th minute, the petri dish would become full.Easy wasn’t it?

When would the petri dish be one third full??

MORE SUDOKU HINTS

Track the digit 9 all through the grid.

If you directly attempt to find 9 in the central box, you should realize that data is insufficient. But be assured all the 9’s are for you to conquer.

What about 2?

By the way, don’t forget the rules of checking columns and rows. Carefully look at the 2nd row from the top: 7 6 2 9 _ 4 _ _ _.

Which are the missing numbers? 1 3 5 and 8.

The top right 3x3 section already has an 8 so the missing terms of the second row in that section cannot have 8.

Easy wasn’t it?

THE COIN CONUNDRUM

Suppose we had just 2 coins, we put them on either side of the balance and whichever side is heavier would have the counterfeit coin.

Even with 3 coins, we would need only one weighing.

Place 1 coin each on the two sides of the pan balance and we have 1 coin left with us.If any coin is heavier in the pan balance, it is the counterfeit coin. But if the two coins balance each other, then obviously the coin with us is the counterfeit coin.

Can you find the counterfeit coin among 4 coins in one weighing? Or would we need a second weighing?

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We set up this crazy set of gears and are about to spin the large, central gear in the clockwise direction?

In which directions would the gears marked 1 & 2 rotate?

GEAR UP

Fill in the blanks below and discover some interesting patterns:

What pattern do you observe?

76923 x 1

76923 x 10

76923 x 9

76923 x 12

76923 x 3

76923 x 4

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=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

76923 x 2

76923 x 7

76923 x 5

76923 x 11

76923 x 6

76923 x 8

And it isn’t over yet! Explore more!

142857 x 1

142857 x 2

142857 x 3

142857 x 4

142857 x 5

142857 x 6

142857 x 7

142857 x 8

MATHEMAGIC

Can you combine the digits from 1 to 9 i.e. 1, 2, 3, 4, 5, 6, 7, 8 and 9 in an expression that equals 100 using any mathematical signs?

1 2 9 = 100

As we were putting together this newsletter and having pizza, an interesting situation came up.

The pizza was to be sliced and served equally among the eight of us.It is easy to do this with four straight cuts.

We did it in just three! Can you figure out how did we do it?

PIZZA PARTY

We were out for some fun-flying and something extraordinary happened.

We marked a spot and flew 100 miles down south.

Then we flew due east for 200 miles before flying due north for 100 miles.

We reached exactly the same spot where we had started from.

FLYING BONKERS

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Where did we mark the spot as we took off? How did we really chart this course?

If we only did things that were easy, we wouldn’t actually be learning anything. We’d just be practicing things we already know.“

-David Dockterman

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1 2 9 = 100

A sample answer:

123 - 45 - 67 + 89 = 100Here’s another one:(1 + 2 + 3 + 4 + 5) x 6 - 7 + 8 + 9 = 100

Find more!

A more involved one:

Here 4! = 4 x 3 x 2 x 1. (This operation is known as the factorial)

FLYING BONKERS

Can such a thing really happen - Two right-angled turns and you reach where you started out?

In 2 D, this is how it would seem.

But interestingly, this isn’t how it happens on Earth, because the Earth is 3 D or three dimensional.Here’s a look at a model of the Earth:

Try plotting our plane’s course on the Earth above.

Does it now seem possible to return to the original location despite having taken two right-angled turns?

Isn’t Earth’s geometry weird?

5 + 5 + 5 = 550

Draw just one straight line to make the above equation true.*You can't touch the = sign.

JUST ONE LINE

- -1 + 2 + 3 + (4! x 5) + 6 - 7 - 8 - 9

ONCE AGAIN… WELCOME TO SPARK!

The monthly 8 - 16 page newsletter / magazine bringing to you: Puzzles | Thought Experiments | Articles | Activities | Mathathons

And even games!

Your participation is paramount & invited!

Every idea, thought, question that comes to your mind deserves to be explored and expressed.

Don’t forget to share your sketches, writings and photos with us.Exciting and intriguing responses might just win you

some amazing gifts and prizes!

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Annual Subscription @ Rs. 750

Send in your replies to spark@qureeus.com

Write the puzzle / article’s heading as the subject line and your name.We’d love to have your photo as well so that your answer has a face too!

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SPARK

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