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Hard Clock Time Puzzle

Hard Clock Time Puzzle Solution - 22 November

At a certain point of time someone observes a clock and find out that the hour hand is exactly at the minute mark and the minute hand is six minutes ahead it. The clock is observed again to find out that hour hand is exactly on a different minute mark but the minute hand is seven minutes ahead of it this time.

Can you calculate the time that has elapsed between the two observations?

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Solution
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Missing Leprechaun Picture Puzzle

Missing Leprechaun Picture Puzzle Solution - 21 November

One of the leprechaun is missing if you see the two pictures attached to this question. Where did he go? When he comes back, do you know where has he been?





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Solution
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Challenging Math Problem

Challenging Math Problem Solution - 20 November

You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you cant go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:

Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10

Now, how many of each must you buy to fulfill the condition given?

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Solution

1 green ball = $6
29 yellow balls = $87
70 black balls = $7

Detailed Explanation : Let us denote the number of balls to be brought with a variable p = green sponges q = yellow sponges r = black sponges Now using a simple expression: p + q + r = 100 6p + 3q + 0.1r = 100 Multiplying the first equation by 6 then 3 and subtracting the two equations, we get: 6p + 6q + 6r = 600 3p + 3q + 3r = 300 3q = 500 - 5.9r 3p = 2.9r - 200 Usually, we have three equations to solve three variables. However, we will manage with just two here because we know that p and q are non-negative integers. If 3q >/= 0, then 500 - 5.9r >/= 0. Using this, r /= 0, then 2.9r - 200 > 0. This implies that r >/= 68.97. Now, the number of black balls must be an even dollar amount or we will land up with a fraction. Considering the expressions, you know that there can be just two integers that can satisfy the condition while lying in between 68.97 and 84.75. If we take r as 80 and solve the equations (the last two equations), we will get p = 10.67 and q = 9.33. But p and q must be integer and not fraction. Thus you can cancel out 80. If we take r as 70, we will get p = 1 and b = 29. Therefore following are the number of balls that we must buy: 1 green ball = $6 29 yellow balls = $87 70 black balls = $7

Mathematical Proof Puzzle

Mathematical Proof Puzzle Solution - 19 November

Below, you will find the mathematical proof that 10 equals 9.99999…. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

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Solution
No error is present in this proof and 10 is actually equal to 9.99999…. The proof is absolutely correct.

Fun Equation Puzzle

Fun Equation Puzzle Solution - 18 November

You are given the sum of symbols in each row and column in the attached figure. Analyzing the figure, can you find out the value of the symbols?



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Solution
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