Crack The 10-Digits Password

In an attempt to further protect his secret chicken recipe, Colonel Sanders has locked it away in a safe with a 10-digit password.  Unable to resist his crispy fried chicken, you'd like to crack the code. 

Try your luck using the following information:

All digits from 0 to 9 are used exactly once.

No digit is the same as the position which it occupies in the sequence.

The sum of the 5th and 10th digits is a square number other than 9.

The sum of the 9th and 10th digits is a cube.

The 2nd digit is an even number.

Zero is in the 3rd position.

The sum of the 4th, 6th and 8th digits is a single digit number.

The sum of the 2nd and 5th digits is a triangle number.

Number 8 is 2 spaces away from the number 9 (one in between).

The number 3 is next to the 9 but not the zero.

Click here to know how to CRACK it! 

Cracking The 10-Digits Password

What was the challenge? 

Let's suppose the 10-digits password is ABCDEFGHIJ.

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Take a look at the given clues to crack down the password.

1. All digits from 0 to 9 are used exactly once.

2. No digit is the same as the position which it occupies in the sequence.

3. The sum of the 5th and 10th digits is a square number other than 9.
 
4. The sum of the 9th and 10th digits is a cube.
 
5. The 2nd digit is an even number.
 
6. Zero is in the 3rd position.
 
7. The sum of the 4th, 6th and 8th digits is a single digit number.
 
8. The sum of the 2nd and 5th digits is a triangle number.
 
9. Number 8 is 2 spaces away from the number 9 (one in between).
 
10. The number 3 is next to the 9 but not the zero. 

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STEPS : 

Respective Clues are in ().

1] Since, every digit is used only once (1), the sum of 2 digits can't exceed 
9 + 8 = 17 and minimum sum of 2 digits can be only 0 + 1 = 1.

2] So, the sum of 5th & 10th digits which is square (3) can be - 1, 4, 16.
The sum of 9th & 10th digits which is cube (4) can be - 1, 8.
The sum of 2nd & 5th digits which is triangle number (8) can be - 1, 3, 6, 10, 15.

3] As per (6), 0 is already at third position i.e. C = 0. Hence, 2nd, 5th, 9th or 10th digits can't be 0. Therefore, the sum of 5th & 10th or 9th & 10th or 2nd & 5th can't be 1. Revising list of possible values of those in step 2.

The sum of 5th & 10th digits which is square (3) can be -  4, 16.
The sum of 9th & 10th digits which is cube (4) can be -  8.
The sum of 2nd & 5th digits which is triangle number (8) can be -  3, 6, 10, 15.

4] Possible pairs of 9th & 10th digits - (1,7), (7,1), (2,6), (6,2), (3,5), (5,3)

If IJ = 71, then 5th digit E must be 4 - 1 = 3 & possible values of 2nd digit B are 0,3,7.
But as per (5), B must be even & C = 0 already.

IJ = 26 or 62 or 35 doesn't leave any valid value for 5th digit E.

If IJ = 53, then 5th digit E must be 1 & possible values of 2nd digit B are 2,5,9
That is B = 2 (5). But as per (2), no digit is the same as the position which it occupies in the sequence. So, the number 2 can't be at 2nd position where B is there.

Hence, IJ must be 17 i.e. I = 1, J = 7.

5] This leaves only 9 as valid value for 5th digit E so that (3) is true. 

So, E = 9 and hence B = 6 with sum of 2nd digit B and 5th digit E as 15.

6] So far, we have, B = 6, C = 0, E = 9, I = 1 and J = 7. 

As per (10), the number 3 is next to the 9 but not the zero. Hence, the 6th digit F must be 3. F = 3.

7] As per (9), the 8 is 2 spaces away from 9 i.e. here 5th digit E=9. With 3rd position already occupied by C = 0, the digit 8 must be at 7th position. 
So, G = 8. 

8] As per (7), D + F + H must be single digit. We have, F = 3 already, 
so possible values of D + H are 0, 1, 2, 3, 4, 5, 6.

D + H can't be 0 (0+0), 1 (1+0), 2(1+1/2+0), 3(1+2/3+0), 4(2+2/3+1/4+0), 5(2+3/4+1/5+0) since digits are repeated with C=0, I=1, F=3 already.

Hence, D + H = 6. 

9] Now, D = 5 and H = 1 is not possible. Also, D/H can't be 0 or 6. Both D and H can't be 3 at the same time. D can't be 4 as D is at 4th position. 

Hence, D = 2, H = 4.

10] With B = 6, C = 0, D = 2, E = 9, F = 3, G = 8, H = 4, I = 1, J = 7, the only digit left for the first position A is 5. So A = 5.

CONCLUSION : 

A = 5, B = 6, C = 0, D = 2, E = 9, F = 3, G = 8, H = 4, I = 1, J = 7.

So, the 10-digits password ABCDEFGHIJ is 5602938417.

 

The Jungle On The Plot of Land

There is a plot of land that is 16 square acres, arranged in a 4 X 4 grid. There are 16 mammals, two each of the following: beaver, cat, dog, goat, horse, lion, tiger, and walrus. There is one mammal in each acre. The acres are labeled A through P, as shown below.

A B C D
E F G H
I J K L
M N O P

Given the following clues, determine where each mammal is located. The terms "next to" and "connected together" mean vertically, horizontally, or diagonally.

1) A and D do not contain the same mammal, but one of them has a dog.

2) E and O do not contain the same mammal, but one of them has a horse.

3) B and L contain the same mammal, but not a tiger.

4) C and M contain the same mammal, but not a beaver.

5) F, K, N, and P are four different mammals.

6) The tigers are in different columns.

7) The goats are located in two of the following locations: B, C, K, and O.

8) The lions are located in two of the following locations: A, E, F, and M.

9) Cats don't get along with dogs, so neither cat is next to a dog.

10) Tigers have goats on their menu, so each tiger must be next to at least one goat and each goat must be next to at least one tiger.

11) The beavers and walruses live on the same body of water, so all four must be connected together in some fashion.

Click to know how animals are located! 

Oraganised Jungle On The Plot of Land

What was the puzzle?

As per given data - 

There is one mammal in each of 16 acres arranged in 4 x 4 grids. The acres are labeled A through P, as shown below.

A B C D
E F G H
I J K L
M N O P

Given the following clues, determine where each mammal is located. The terms "next to" and "connected together" mean vertically, horizontally, or diagonally.

1) A and D do not contain the same mammal, but one of them has a dog.

2) E and O do not contain the same mammal, but one of them has a horse.

3) B and L contain the same mammal, but not a tiger.

4) C and M contain the same mammal, but not a beaver.

5) F, K, N, and P are four different mammals.

6) The tigers are in different columns.

7) The goats are located in two of the following locations: B, C, K, and O.

8) The lions are located in two of the following locations: A, E, F, and M.

9) Cats don't get along with dogs, so neither cat is next to a dog.

10) Tigers have goats on their menu, so each tiger must be next to at least one goat and each goat must be next to at least one tiger.

11) The beavers and walruses live on the same body of water, so all four must be connected together in some fashion. 

STEPS : 

1] As per Hint 3, blocks B & L contains the same mammal.  As per Hint 4, blocks C & M have the same mammal. So, as per Hint 7 suggests, the goats must be in K & O because if they are in B & C then L & M also supposed to have them but there are total 2 goats only. K - GOAT, O - GOAT

2] If O has a goat then as per Hint 2, E must have a horse.  E - HORSE

3] As per Hint 8, if Lion is located at M then as per Hint 3 the second lion must be in B. But Hint 8 doesn't list B as possible location of lions. Hence, it must not be in M. Also, E is already occupied by horse, hence lions must be at A & F.
A - LION, F - LION

4] So if A has lion, then as per Hint 1, D must have a dog. D - DOG

5] Since C is just near to the D having a dog, as per Hint 9, C can't have cats. As per Hint 10, tigers should be in the 3x3 grids around the goats and goats are located at K and O. But M is out of these grids, hence must not have tigers.

6] And as per Hint 4, C & M having same mammal, but not beaver. As deduced above, it can't be cats or tigers either. With 1 dog already at D, 1 Horse at E, both C & M can't have dogs or horses. Hence, C & M must have walruses (only left mammal out of 8 kind of mammals). C - WALRUS, M - WALRUS

7] As per Hint 11, for walruses (at C & M) to be connected with beavers in some fashion, they must be at G and J. So, G & J have beavers.
G - BEAVER, I - BEAVER

8] Since Hint 3 suggests that B & L are not having tigers, the only animals left in terms of numbers of 2 for to be at B & L are cats. So B & L have cats. B - CAT, L - CAT

9] So far, we have, A - Lion, B - Cat, C - Walrus, E - Horse D - Dog, F - Lion, 
G -  Beaver, J - Beaver, K - Goat, L -  Cat, M - Walrus, O - Goat. Blocks left are  H, I, N, P

10] As per Hint 10 & with goats at K and O, tigers can't be at I. So possible blocks for tigers are H, N and P.

11] But as per Hint 6, tigers has to be in different columns and H & P are in the same column. Also, as per Hint 5, N & P can't have same mammals. And since, H & P falls under same column, the tigers must be occupying N and H. 
 H -  TIGER, N - TIGER

12] Since one cat is at L, P can't be a dog. Hence, I must be having a dog and P must be having a horse.  I - DOG, P - HORSE.

SUMMARY : 

A = lion, B = cat, C = walrus, D = dog
E = horse, F = lion, G = beaver, H = tiger
I = dog, J = beaver, K = goat, L = cat
M = walrus, N = tiger, O = goat, P = horse

 

The Third Case of Mystery Number

There is a ten-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. 

Given the following clues, what is the number?

1) Digit A is either a square number or a triangle number, but not both.

2) Digit B is either an even number or a cube number, but not both.

3) Digit C is either a cube number or a triangle number, but not both.

4) Digit D is either an odd number or a square number, but not both.

5) Digit E is either an odd number or a cube number, but not both.

6) Digit F is either an odd number or a triangle number, but not both.

7) Digit G is either an odd number or a prime number, but not both.

8) Digit H is either an even number or a square number, but not both.

9) Digit I is either a square number or a cube number, but not both.

10) Digit J is either a prime number or a triangle number, but not both.

11) A < B, C < D, E < F, G < H, I < J

12) A + B + C + D + E < F + G + H + I + J

Here is that MYSTERY number!


The FIRST Case of Mystery Number

The SECOND Case of Mystery Number 

Demystifying The Third Mystery Number

What was the challenge?

Taking a look at the given clues first for identifying the mystery number ABCDEFGHIJ.

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1) Digit A is either a square number or a triangle number, but not both.

2) Digit B is either an even number or a cube number, but not both.

3) Digit C is either a cube number or a triangle number, but not both.

4) Digit D is either an odd number or a square number, but not both.

5) Digit E is either an odd number or a cube number, but not both.

6) Digit F is either an odd number or a triangle number, but not both.

7) Digit G is either an odd number or a prime number, but not both.

8) Digit H is either an even number or a square number, but not both.

9) Digit I is either a square number or a cube number, but not both.

10) Digit J is either a prime number or a triangle number, but not both.

11) A < B, C < D, E < F, G < H, I < J

12) A + B + C + D + E < F + G + H + I + J  

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STEPS  :

Even numbers between 0 to 9 - 0, 2, 4, 6, 8

Odd numbers between 0 to 9 - 1, 3, 5, 7, 9

Square numbers between 0 to 9 - 0, 1, 4, 9 

Cube numbers between 0 to 9 - 8.

Prime numbers between 0 to 9 - 2, 3, 5, 7

Triangle numbers between 0 to 9 - 0, 1, 3, 6

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STEP 1 : 

A can't be 0 as no leading 0's in the mystery number ABCDEFGHIJ.

Remember both of hints can't be true at the same time. That is Digit A is either a square or a triangle number but not both. Since, 0 and 1 are square as well as triangle numbers, A can't be 0 or 1. 

Similarly, 8 is even as well as cube, B can't take 8. And so on.

Possible values of A -  3, 4, 6, 9. (Square/Triangle)

Possible Values of B - 0, 2, 4, 6. (Even/Cube).

Possible Values of C - 0, 3, 6, 8. (Cube/Triangle)

Possible Values of D - 3, 4, 5, 7. (Odd/Square)

Possible Values of E - 3, 5, 7, 8. (Odd/Cube)

Possible Values of F - 0, 5, 6, 7, 9 (Odd/Triangle)

Possible Values of G - 1, 2, 9 (Odd/Prime)

Possible Values of H - 0, 2, 6, 8, 9 (Even/Square)

Possible Values of I -  4, 8, 9 (Square/Cube)

Possible Values of J -  0, 1, 2, 5, 6, 7  (Prime/Triangle) 

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STEP 2 :

The value of I can't be 8 or 9 as there will be no digit left for J which is greater than I. 

Hence, I = 4.
 
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STEP 3 : 

Digit A can't be 6 or 9 since no digit will be left for B>A. 

As we have, I = 4, the digit A = 3 and hence B = 6.

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STEP 4 :

The only digit left for C is 0, i.e. C = 0 as C can't be 8 for C<D to be true.

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STEP 5 :

  Since I = 4 itself, so digit J can't be 0, 1, 2 for I<J to be true.

Digit D and digit J take either take 5 or 7. With that the only valid digit left for E is 8 to satisfy the condition E<F. 

Hence E = 8.

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STEP 6 :

If E = 8, then F has to be 9. So, F = 9.
 
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STEP 7 : 

With 6, 8, 9 already taken up by other letters, the only digit left for H is 2 for G<H to be true. So, H = 3 and hence G = 1.

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STEP 8 :

As per condition 12, 

A + B + C + D + E < F + G + H + I + J 

3 + 6 + 0 + D + 8 < 9 + 1 + 2 + 4 + J

17 + D < 16 + J 

As deduced in STEP 4, D must be 5 or 7 and J must be 7 or 5.

For above equation to be true, D = 5 and J = 7.


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Conclusion :

A = 3, B = 6, C = 0, D = 5, E = 8, F = 9, G = 1, H = 2, I = 4, J = 7

Hence, the number ABCDEFGHIJ must be 3605891247.

Verifying the given hints - 

1) 3 is a triangle number, but not a square number.
2) 6 is an even number, but not a cube number.
3) 0 is a cube number, but not a triangle number.
4) 5 is an odd number, but not a square number.
5) 8 is a cube number, but not an odd number.
6) 9 is an odd number, but not a triangle number.
7) 1 is an odd number, but not a prime number.
8) 2 is an even number, but not a square number.
9) 4 is a square number, but not a cube number.
10) 7 is a prime number, but not a triangle number.
11) 3 < 6, 0 < 5, 8 < 9, 1 < 2, 4 < 7
12) 3 + 6 + 0 + 5 + 8 = 22, 9 + 1 + 2 + 4 + 7 = 23, 22 < 23  

40 Matchsticks Challenge!

The diagram below shows 40 matchsticks arranged in a square grid.

What is the fewest number of matchsticks that need to be removed so that there are no squares (of any size) remaining?


This is how it can be done! 

Eliminating Square in 40 Matchsticks Challenge!

What was the challenge?

All that we need to do is that remove these differently colored 9 matchsticks.

So we get, 

There can be other variations of this answer but we have to remove 9 matchsticks at least to make sure there is no square.

Four Glasses Puzzle

Four glasses are placed on the corners of a square table. Some of the glasses are upright (up) and some upside-down (down). A blindfolded person is seated next to the table and is required to re-arrange the glasses so that they are all up or all down, either arrangement being acceptable, which will be signaled by the ringing of a bell. 

The glasses may be re-arranged in turns subject to the following rules. 

1.Any two glasses may be inspected in one turn and after feeling their orientation the person may reverse the orientation of either, neither or both glasses.

2.After each turn the table is rotated through a random angle. 

3.The puzzle is to devise an algorithm which allows the blindfolded person to ensure that all glasses have the same orientation (either up or down) in a finite number of turns. The algorithm must be non-stochastic i.e. it must not depend on luck.

Here is that algorithm!