7 Additions and 1 Subtraction

Fill the boxes below with only 7 addition (+) and 1 subtraction (-) operators. 

The smartest way to find the right place 

Correct Placement of Subtraction Operator

This was the question!

For a moment. let's put '+' operator in all given boxes.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 33.

Let 'x' be the number ahead of which '-' should be there where x can be any number from 1 to 9. 

In above addition the x is already (unknown value) added so first we need to subtract it twice from LHS; first to compensate the addition operation & second for the mandatory subtraction operator that is to be placed at right place.

So for example, if it's ahead of 4 as right place then

1 + 2 + 3 + 4 - 4 - 4 + 5 + 6 + 7 + 8 + 9 = 33.

1 + 2 + 3 + (4 - 4) - 4 + 5 + 6 + 7 + 8 + 9 = 33.

For x, which is already there & can be any from 1 to 9,

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9  - x - x = 33. 

45 - 2x = 33

2x = 12

x = 6.

Hence, the subtraction (-) sign should be ahead of 6. 

The River Crossing Challenge!

There are 3 men, two Chimps, and one Gorilla on one side of a river :

• They have a boat but only the men and the Gorilla can row the boat across, so there must always be a human and/or Gorilla on the boat.

• The boat can only carry two people/monkeys.

• If monkeys and humans are together on one side of the river there must be as many or more people than monkeys for the men's safety. 

How can all men and monkeys make it to the other side ? 



Here is the PROCESS by which it can be done! 

Responding to The River Crossing Challenge!

What was the challenge ahead?

Recalling the conditions those need to be followed. 

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• They have a boat but only the men and the Gorilla can row the boat across, so there must always be a human and/or Gorilla on the boat.

• The boat can only carry two people/monkeys.

• If monkeys and humans are together on one side of the river there must be as many or more people than monkeys for the men's safety.

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Here, we go step by step process. (M - Men, G - Gorilla, C - Chimps)

1. The gorilla takes 1 chimp across the river and comes back. 

    (M - 3, G - 1, C - 1 | M - 0, G - 0, C - 1) 

2. Again, gorilla takes 1 man across the river and comes back. 

    (M - 2, G - 1, C - 1 | M - 1, G - 0, C - 1)

Now, here gorilla can't take chimp across the river as that will violate condition 3 on that side. Neither gorilla can take 1 man on other side and return back since number of monkeys on returning side will be more than people again violating condition 3.

3. Next, one man drops gorilla at the other side and bring back chimp.

    (M - 2, G - 0, C - 2 | M - 1, G - 1, C - 0) 

4. Now, 2 men has to cross the river and send back gorilla for the rest of work.

   (M - 0, G - 1, C - 2 | M - 3, G - 0, C - 0) 

5. Finally, gorilla takes 2 chimps across the river in 2 round trips.

   (M - 0, G - 0, C - 0 | M - 3, G - 1, C - 2) 

 

Puzzle : The Fake Coin Challenge!

There are 101 coins out of which 1 is fake, the fake coin is identical to a genuine coin but differs in weight. Using weight balance only twice how can we determine whether the fake coin is heavier or lighter than a genuine coin?

 

 

This is how to do it! 

Fake Vs Genuine Coin Weigh Comparison

This was the challenge!

Remember we are asked to determine whether the fake coin is lighter or heavier when compared with the genuine coin and not to identify the fake coin itself.

Keep aside any one coin. Divide remaining 100 coins into 2 groups of 50 coins each. Put these 2 groups on 2 pans of the balance.

1. If they weigh equal the the coin that is kept aside is fake. Weigh it against any genuine among 100 coins to know whether fake coin is lighter or heavier than genuine.

2. If they are not equal then that means the fake coin either made one side heavier or the other side lighter.

3. Take the heavier group of 50 coins for the next test. Divide them into 2 groups of 25 coins each. 

4. Put 25 - 25 coins on weighing balance. If they weigh equal then that means no fake coin among them which also means the fake coin was in the other group of 50 coins which was lighter in the first weighing. 

Hence, the fake coin is lighter present in the other group of 50 coins making the group slightly lighter compared to group of 50 genuine coins.

4.1. And if the result of weighing 25 - 25 coins is unequal then it's clear that the fake coin is among these 50 coins. Also, it must be heavier making this group to weigh more than the other group of 50 genuine coins in the first weighing.

This way, we can determine whether the fake coin is heavier or lighter than genuine one using the weighing balance only twice.

Find The Heaviest Ball

Given 27 table tennis balls, one is heavier than the others.

What is the minimum number of weighings (using a two-pan balance scale) needed to guarantee identifying the heavy one? The other 26 balls weigh the same.

Here is how to identify the heavier ball.