An "IQ test" puzzle image is shown. The puzzle presents a series of equations with a hidden pattern:

 

An "IQ test" puzzle image is shown. The puzzle presents a series of equations with a hidden pattern:

• $152=15$

• $153=30$

• $154=45$

• $155=60$

• $156=75$

• $159=???$

The user wants an article explaining the solution to this puzzle.

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Unlocking the Logic Puzzle

This type of puzzle, often shared online as an "IQ test" or brain teaser, relies on finding a simple, non-mathematical pattern rather than complex calculations. The key is to look at how the number on the left transforms into the number on the right.

At first glance, the equations look incorrect, but the solution lies in rethinking the numbers themselves.

The Pattern

The solution to this puzzle is to ignore the first two digits of the three-digit number on the left. The pattern is based solely on the last digit. The answer on the right is then the product of the last digit of the left-hand number and the number 15.

Let's break it down:

• For 152 = 15, the last digit is 2. The pattern is not immediately obvious from this line, as 2 times 15 is 30, not 15. The puzzle is designed to make you think differently. The trick is to see that the solution for 152 is not given, but rather the solution for 153 is given as 30, for 154 as 45, etc. The puzzle starts from the number 152 for no other reason than to confuse the solver.

Let's focus on the pattern:

• 153: The last digit is 3. Multiply it by 15. $3\times 15=45$. But the puzzle says $153=30$.

• 154: The last digit is 4. Multiply it by 15. $4\times 15=60$. But the puzzle says $154=45$.

• 155: The last digit is 5. Multiply it by 15. $5\times 15=75$. But the puzzle says $155=60$.

This shows that the pattern is not as simple as multiplying the last digit by 15. Let's look at a different approach.

The value on the right is the product of the last digit of the left-hand number and a number that increases by one with each line.

Let's see:

• 152: last digit is 2. $2\times ?=15$.

• 153: last digit is 3. $3\times ?=30$.

• 154: last digit is 4. $4\times ?=45$.

• 155: last digit is 5. $5\times ?=60$.

• 156: last digit is 6. $6\times ?=75$.

This also does not work.

The real pattern

The pattern is a bit more obscure than what one would normally expect from this kind of puzzle.

The number on the right increases by 15 with each line. The number on the left increases by 1.

• $152=15$

• $153=30$ ($15+15$)

• $154=45$ ($30+15$)

• $155=60$ ($45+15$)

• $156=75$ ($60+15$)

The solution is to keep adding 15 to the previous answer until you get to the 159 row.

• $157=90$ ($75+15$)

• $158=105$ ($90+15$)

• $159=120$ ($105+15$)

The puzzle is trying to trick you into finding a relationship between the numbers on the left and the numbers on the right, but the relationship is purely between the numbers on the right themselves.

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The Final Answer

Following this pattern, the final answer for $159=???$ is 120.