science

Maris–McGwire–Sosa pair

Maris–McGwire–Sosa pair is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Maris–McGwire–Sosa pair rather than just read about it. In short: In recreational mathematics, Maris–McGwire–Sosa pairs (MMS pairs, also MMS numbers) (sequence A045759 in the OEIS) are two consecutive natural numbers such that adding each number's digits (in base 10) to the digits of its prime factorization gives the same sum. Thus 61 → 6 + 1 (the sum of its digits) + 6 + 1 (since 61 is its prime factorization) and 62 → 6 + 2 (the sum of its digits) + 3 + 1 + 2 (since 31 × 2 is it…

Key takeaways

Maris–McGwire–Sosa pair belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Maris–McGwire–Sosa pair to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Maris–McGwire–Sosa pair from memory before moving on to harder problems.

Reference excerpt

In recreational mathematics, Maris–McGwire–Sosa pairs (MMS pairs, also MMS numbers) (sequence A045759 in the OEIS) are two consecutive natural numbers such that adding each number's digits (in base 10) to the digits of its prime factorization gives the same sum.

Thus 61 → 6 + 1 (the sum of its digits) + 6 + 1 (since 61 is its prime factorization) and 62 → 6 + 2 (the sum of its digits) + 3 + 1 + 2 (since 31 × 2 is its prime factorization). The above two sums are equal (= 14), so 61 and 62 form an MMS pair. MMS pairs are so named because in 1998 the baseball players Mark McGwire and Sammy Sosa both hit their 62nd home runs for the season, passing the old record of 61, held by Roger Maris. American engineer Mike Keith noticed this property of these numbers and named pairs of numbers like these MMS pairs.

Worked examples

Example 1 — a first encounter with Maris–McGwire–Sosa pair

Start with the simplest possible case. Write down what Maris–McGwire–Sosa pair claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Maris–McGwire–Sosa pair before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Maris–McGwire–Sosa pair ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Maris–McGwire–Sosa pair

In research: Maris–McGwire–Sosa pair appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Maris–McGwire–Sosa pair in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Maris–McGwire–Sosa pair is common in secondary-school and first-year university syllabi. It links to neighbouring topics Base-dependent integer sequences, so understanding it makes those chapters shorter.
In everyday life: Look for Maris–McGwire–Sosa pair outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Maris–McGwire–Sosa pair in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Maris–McGwire–Sosa pair means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Maris–McGwire–Sosa pair out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Maris–McGwire–Sosa pair in simple terms?

Why does Maris–McGwire–Sosa pair matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Maris–McGwire–Sosa pair?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Maris–McGwire–Sosa pair.