(Puzzles) Challenging Mathematical Puzzles (19)
Puzzles : Challenging Mathematical Puzzles
54. A man has Ten Horses and nine stables as shown here.
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The man wants to fit Ten Horses into nine stables. How can he fit Ten horses into nine stables?
Answer :-
The answer is simple. It says the man wants to fit "Ten Horses" into nine stables. There are nine letters in the phrase "Ten Horses". So you can put one letter each in all nine stables.
[T] [E] [N] [H] [O] [R] [S] [E] [S]
55. A man is at a river with a 9 gallon bucket and a 4
gallon bucket. He needs exactly 6 gallons of water.
How can he use both buckets to get exactly 6 gallons of water?
Note that he cannot estimate by dumping some of the water out of the 9 gallon
bucket or the 4 gallon bucket
Answer
For the sack of explanation, let's identify 4 gallon bucket as Bucket P and 9
gallon bucket as Bucket Q.
Operation |
4
gallon bucket |
9
gallon bucket |
Initially |
0 |
0 |
Fill the bucket Q with 9 gallon water |
0 |
9 |
Pour 4 gallon water from bucket Q to bucket P |
4 |
5 |
Empty bucket P |
0 |
5 |
Pour 4 gallon water from bucket Q to bucket P |
4 |
1 |
Empty bucket P |
0 |
1 |
Pour 1 gallon water from bucket Q to bucket P |
1 |
0 |
Fill the bucket Q with 9 gallon water |
1 |
9 |
Pour 3 gallon water from bucket Q to bucket P |
4 |
6 |
9 gallon bucket contains 6 gallon of water, as required.
56. Each of the five characters in the word BRAIN has a different value between 0 and 9. Using the given grid, can you find out the value of each character?
B R A I N 31
B B R B A 31
N I A B B 32
N I B A I 30
I R A A A 23
37 29 25 27 29
The numbers on the extreme right represent the sum of the values represented by the characters in that row. Also, the numbers on the last raw represent the sum of the values represented by the characters in that column. e.g. B + R + A + I + N = 31 (from first row)
Answer :-
B=7, R=6, A=4, I=5 and N=9
Make total 10 equations - 5 for rows and 5 for columns - and sovle them.
From Row3 and Row4,
N + I + A + B + B = N + I + B + A + I + 2
B = I + 2
From Row1 and Row3,
B + R + A + I + N = N + I + A + B + B - 1
R = B - 1
From Column2,
R + B + I + I + R = 29
B + 2R + 2I = 29
B + 2(B - 1) + 2I = 29
3B + 2I = 31
3(I + 2) + 2I = 31
5I = 25
I = 5
Hence, B=7 and R=6
From Row2,
B + B + R + B + A = 31
3B + R + A = 31
3(7) + 6 + A = 31
A = 4
From Row1,
B + R + A + I + N = 31
7 + 6 + 4 + 5 + N = 31
N = 9
Thus, B=7, R=6, A=4, I=5 and N=9