## Tell Me Your Shoe Size, and I will Estimate Your Age!

I had better say something here about this question of age, since it is particularly important for mathematicians. . . . To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. We can naturally find much more striking illustrations. We may consider, for example, the career of a man who was certainly one of the world’s three greatest mathematicians. Newton gave up mathematics at fifty, and had lost his enthusiasm long before; he had recognized no doubt by the time he was forty that his greatest creative days were over. His greatest idea of all, fluxions and the law of gravitation, came to him about 1666 , when he was twenty four—’in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since’. He made big discoveries until he was nearly forty (the ‘elliptic orbit’ at thirty-seven), but after that he did little but polish and perfect.

G. H. Hardy

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Are you intrigued by the idea that something as simple as a shoe size could reveal clues about a person’s age? This intriguing mathematical puzzle challenges common assumptions and takes us on a journey into the world of numbers and relationships.

The puzzle begins with the seemingly unrelated connection between shoe size and age. Is there really a correlation, or is it just a coincidence? When you think about it, there’s a logical link between age and shoe size. As we grow older, our feet tend to grow as well. But can we quantify this relationship? Can we create a formula or a rule that allows us to estimate someone’s age based solely on their shoe size? All you need to do is follow the instructions carefully and use a calculator if you wish!

Note. This is valid with respect to the year 2023 only! Please make the necessary adjustments in step 5 for other years, as appropriate. Additionally, this trick is applicable if your age is less than 100.

Consider the following two examples.

Information Required: We require information about your birth year and shoe size. Let’s assume that y represents the birth year, and s represents the shoe size.

Let’s assume that the birthday has already occurred.

Step 1: We will approximate the value of s to the nearest integer (for instance, 3, 5, 10, etc.).

Step 2: When we multiply s by 5, we obtain 5s.

Step 3: Adding 50 to 5s results in 5s + 50.

Step 4: Next, by multiplying by 20, we get

(5s + 50) × 20

= 100s + 1000.

Step 5: Since the birthday has already occurred, we add 1023 to get

100s + 1000 + 1023

= 100s + 2023.

Step 6: By subtracting the birth year y, we finally arrive at

(100s + 2023) – y

= 100s + (2023 – y).

Clearly, (2023 – y) represents our current age. Hence, the final result is always 100s added to our age.

Now, assuming that the birthday is yet to happen. Everything will remain the same; the only change will occur in steps 5 and 6.

Step 5: Since the birthday has not yet occurred, we add 1022 to get

100s + 1000 + 1022

= 100s + 2022.

Step 6: By subtracting the birth year y, we finally obtain

(100s + 2022) – y

= 100s + (2022 – y).

Clearly, (2022 – y) represents our present age.

Thus, the final result is always 100s added to our age.

So, whether you’re a math enthusiast, a puzzle lover, or simply someone intrigued by the mysteries of age and shoe size, this mathematical puzzle offers an engaging and intellectually stimulating challenge. As you explore the potential connections and work to develop your estimation methods, you’ll discover the beauty of mathematics in uncovering hidden relationships and making sense of the world around us.

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