**Question**

**Introduction**

This puzzle is making its rounds on the Internet. The “solution” is easy enough.

3 ×
6 = 18

4 ×
8 = 32

5 × 10 = 50

6 × 12 = 72

7 × 14 = 98

Notice that the numbers in the second column is
always twice the corresponding number in the first column. For the number 10, we have

10 × 20 = 200

**Critique 1**

A few people might get tricked by taking 10 × 16 =
160, since 16 is the next even number
after 14. But that is not my gripe. My issue is with the abuse of the “=”
sign. This sign stands for “equal” which
means, equal (Surprise! Surprise!). Equal means the same, having the same
value. 3
is not equal to 18. So we should not write “3 = 18”, because that
is not true. Writing “3 × 6 = 18” is OK and correct, because it makes
sense and it is a true statement.

**Mathematics is not a jumble of nonsensical symbols**, although to some people it seems like it.**The symbols have**. And these symbols should not be abused. If you want to say “*meanings**corresponds to*”, then you might want to use an arrow e.g. “3 ¾® 18”. This is keeping with the modern concept of a*function*, in which a value is assigned unambiguously to another number. Using a function notation we can write things like “f(3) = 18”.**Critique**

**2**

Another problem with puzzles such as this is that, using Lagrange Interpolation
or Newton Interpolation and the like, it is always possible to invent a function that
hits the given first few numbers and then any number you like (even a “wrong”
number). For the above puzzle, the
Lagrange method allows us to cook up a function like this:-

This
function looks complicated, but if you note carefully, when you substitute the
numbers 3, 4, 5, 6, 7 and 10, one of the algebraic fractions with

*x*becomes equal to 1 and the rest of them become 0. Thus, we easily see that f(3) = 18, f(4) = 32, f(5) = 50, f(6) = 72 and f(7) = 98. For f(10), I could actually have chosen any value I like, but I chose the number 42. So the correct answer does not have to be 200. There is actually no single correct answer, since you can make it*any*answer you like! This trick can be done on all similar puzzles, and hence**these “IQ” puzzles have now been effectively debunked**!
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