Crack And Win $500,000 - Puzzle

You are in a game show with four other contestants. The objective is to crack the combination of the safe using the clues, and the first person to do so will win $500,000.

The safe combination looks like this:

??-??-??-??

A digit can be used more than once in the code, and there are no leading zeroes.

Here are the clues:

1. The third set of two numbers is the same as the first set reversed.

2. There are no 2's, 3's, 4's or 5's in any of the combination.

3. If you multiply 4 by the third set of numbers, you will get the fourth set of numbers.

4. If you add the first number in the first set with the first number in the second set you will get 8.

5. The second set of numbers is not greater than 20.

6. The second number in the second set multiplied by the second number in the fourth set equals one higher than the numbers in the first set.

And get moving, I think another contestant has almost figured it out!

Click here for the SOLUTION! 

Crack And Win $500,000 Puzzle - Solution

What was the puzzle?

We know, the safe has a lock having 4 sets of 2 digits as -

?? - ?? - ?? - ??

Since, leading zeros are not allowed any of the set can't be started with 0 like 01, 07, 09 etc. 

Take a look at the clues given - 

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1. The third set of two numbers is the same as the first set reversed.

2. There are no 2's, 3's, 4's or 5's in any of the combination.

3. If you multiply 4 by the third set of numbers, you will get the fourth set of numbers.

4. If you add the first number in the first set with the first number in the second set you will get 8.

5. The second set of numbers is not greater than 20.

6. The second number in the second set multiplied by the second number in the fourth set equals one higher than the numbers in the first set.


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STEPS :

1] As per clue (2), digits 2, 3, 4 or 5 aren't allowed in any set. That means only digits 0, 1, 6, 7, 8, 9 are allowed for sure.

2] For (3) to be true, possible combinations of 3rd and 4th sets are - 

10 x 4 = 40
11 x 4 = 44
16 x 4 = 64
17 x 4 = 68
18 x 4 = 72
19 x 4 = 76

The third set can't be 10 for 2 reasons. - 1} As per clue (1), the first set will be 01 and leading 0's are not allowed. 2} The 4th set will have digit 4 which is not allowed.

The third set can't start with 2X, 3X, 4X or 5X as those digits aren't allowed. Moreover, it can't be started with 6X, 7X, 8X as in that case the value of the 4th set will exceed it's maximum possible value of 96 (if digit 2 was allowed) or 76.

Out of all above combinations, only 17 x 4 = 68 and 19 x 4 = 76 are valid combination as rest of combinations have digits that aren't allowed.

So, one thing is sure that the first digit of the third set is 1. And hence the first digit of first set also must be 1 as per clue (1).

3] As per clue (5), the second set can't exceed 20. It can't start with 0. Hence, possible values ranges from 10 to 19. That means, the first digit of the second set is also 1.

4] Now as per clue (4), if you add the first number in the first set with the first number in the second set you will get 8. That means the first number of first set is 8 - 1 = 7. 

As of now, the code looks like : 71 - 1? - 1? - ??

5] If 7 is the first digit of first set then as per clue (1), 7 itself is second digit of the third set.

Now, the code looks as : 71 - 1? - 17 - ??

6] As per clue (3) and rightly deduced as a possible combinations for 3rd & 4th set in STEP 2, the 4th set must be 17 x 4 = 68.

With that, code turns into : 71 - 1? - 17 - 68.

7] Finally, as per clue (6), the second number in the second set multiplied by the second number in the fourth set equals one higher than the numbers in the first set. This multiplication i.e. ? x 7 must be equal to 71 + 1 = 72. 
Hence, ? = 9.

The final code looks like : 71 - 19 - 17 - 68.

  

"How Did They Cross The River?"

Five men and five dogs (each man owned a dog) went hiking. They encountered a river that was swift and deep. The only way to cross it was an abandoned boat, left ashore on their side. But it would only hold three living things. 

Unfortunately, the dogs were edgy and could not be near another person (not even momentarily) unless its owner was present. One of the dogs attended a highly advanced, highly specialized obedience school and therefore knew how to operate the boat (as the men did) -- the other dogs lack this skill. 

How did the five men and the five dogs cross the river?

THIS is how they accepted the challenge! 

The Challenge of River Crossing

What was the challenge?

Let's name five men as M1, M2, M3, M4, M5 & five dogs as D1, D2, D3, D4, D5.
Assume D1 be the dog having advanced skills of operating boat.

TRAVEL CHART :

1] The dog D1 rows D2, D3 across the river and returns back. After returning back D1 takes D4 across the river & returns back once again.

START : D1-M1, D5-M5, M2, M3, M4  DESTINATION : D2, D3, D4

2] Now, M2, M3 and M4 cross river.

START : D1-M1, D1-M5  DESTINATION : D2-M2, D3-M3, D4-M4

3] Someone from DESTINATION needs to return back to allow others at START to cross the river. So, D4-M4 returns and D1-M1 cross the river. 

START : D4-M4, D5-M5  DESTINATION : D1-M1, D2-M2, D3-M3

4] After D1-M1 reaches to the DESTINATION, D3-M3 returns back.

START : D3-M3, D4-M4, D5-M5  DESTINATION : D1-M1, D2-M2

5] Now, M3, M4 and M5 cross the river.

START : D3, D4, D5  DESTINATION : D1-M1, D2-M2, M3, M4, M5.

6] Finally, the dog D1 at the DESTINATION returns back and makes 2 trips to take D3, D4 and D5 across the river.

START : None  DESTINATION : D1-M1, D2-M2, D3-M3, D4-M4, D5-M5.

This way, five men and five dog cross the river successfully.

The Discounted Purchases : Puzzle

Until last week, Mandy had been putting off the purchase of four major items for her home, waiting for her town's annual bargain days. Each year, the town's four main stores (including Nickels) each send out a coupon for a different percentage discount (10%, 15%, 20%, or 30%) on the purchase of a single item. Can you find the discount that Mandy received on each of her buys, and determine from which store she purchased each item?

Given:

Discounts      : 10%, 15%, 20%, 30%
Store Names : Stears, Pal-Mart, Nickels, Dullard's
Appliances    : Computer, Dishwasher, Lawnmower, VCR

Clues:

1) The percentage discount Mandy received on her new computer was twice that of the item she bought at Dullard's. 

2) The discount on the Stears purchase was ten percentage points lower than the one on the riding lawnmower. 

3) The discount on the dishwasher wasn't 15%. 

4) Pal-Mart, (which didn't issue the 30% off coupon) isn't the store at which Mandy purchased the VCR.

Click here for SOLUTION!

The Discounted Purchases Puzzle : Solution

What was the challenge?

First let's have a given data.

Given:

Discounts: 10%, 15%, 20%, 30%
Store Names: Stears, Pal-Mart, Nickels, Dullard's
Appliances: Computer, Dishwasher, Lawnmower, VCR

Clues:

1) The percentage discount Mandy received on her new computer was twice that of the item she bought at Dullard's. 

2) The discount on the Stears purchase was ten percentage points lower than the one on the riding lawnmower. 

3) The discount on the dishwasher wasn't 15%. 

4) Pal-Mart, (which didn't issue the 30% off coupon) isn't the store at which Mandy purchased the VCR. 

 STEPS : 

1] As per clue (1), Dullard's didn't sell computer to Mandy and she didn't receive 10% or 15% off on computer. Also, Dullard's didn't offer her 20% or 30%.

2] The clue (2) suggests that the lawnmower wasn't purchased at 10% or 15% discount. Also, Stears discount must be 10% or 20%. And Stear didn't sell lawnmower for sure.

3] The clue (3) suggests that dishwasher wasn't sold at 15% discount. So, it's clear that Stears must have sold dishwasher at 10%/20% discount and Dullard's must have sold VCR at 15% discount. Therefore, computer must had been bought with 30% discount.

4] And hence, lawnmower at 20%. With that, Stears must have sold dishwasher at 10% discount as per clue (3).

5] Finally, as per clue (4), Pal-Mart didn't offer 30% discount suggests that it must not have sold computer. Therefore, Nickels sold computer at 30% discount and Pal-Mart sold lawnmower at 20% discount.

CONCLUSION : 

Final summary of the all purchases in form of table looks as - 

Make it 50-50 in Two!

You have three jugs:

A 10-liter jug, filled with water
A 7-liter jug, empty
A 3-liter jug, empty

Your objective is to end up having 5 liters of water in the 10-liter jug, and 5 liters of water in the 7-liter jug.

Note that you have nothing else at your disposal other than these three jugs and that you cannot perform measurements by eye or based on the shape of the jugs.

THIS is how it can be done!