In the following number series, exactly one number is incorrect. Identify the wrong number:

$$11, 75, 11, 136, 87, 303, 268$$

Question

In the following number series, exactly one number is incorrect. Identify the wrong number:

$$11, 75, 11, 136, 87, 303, 268$$

Accepted Answer

**Solution:**

1. Observe the series: $$11, 75, 11, 136, 87, 303, 268$$

2. Check for any pattern or relation between alternate numbers or consecutive numbers.

3. Notice that the first and third numbers are both 11, which might indicate a pattern involving repetition or a relation between alternate terms.

4. Look at the differences or ratios between numbers:
   - From 11 to 75: increase by 64
   - From 75 to 11: decrease by 64
   - From 11 to 136: increase by 125
   - From 136 to 87: decrease by 49
   - From 87 to 303: increase by 216
   - From 303 to 268: decrease by 35

5. The increments 64, 125, 216 are perfect cubes: $$4^3=64, 5^3=125, 6^3=216$$.

6. The decrements should also follow a pattern of perfect squares decreasing:
   - 64 (from 75 to 11) is $$8^2$$
   - 49 (from 136 to 87) is $$7^2$$
   - 35 (from 303 to 268) is not a perfect square, which breaks the pattern.

7. The last decrement should be $$6^2 = 36$$ instead of 35.

8. So, the last number should be $$303 - 36 = 267$$ instead of 268.

**Answer:** 268 is the wrong number in the series.

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