The Viral Meme 9 + 10 = 21 Solved – Mind Your Decisions

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A number of years in the past this equation unfold in Vines and on the web:

9 + 10 = 21

It isn’t true in the usual base 10 decimal system. However what if we modify the equation a bit with different quantity bases? Suppose the numbers on the left are in base x and the quantity on the appropriate is in base y:

(9 + 10) (base x) = 21 (base y)

For what values of x and y is that this equation true? That is really a enjoyable little downside. Watch the video for an answer.

9 + 10 = 21. Viral Meme Solved!

Or hold studying. . .

“All might be properly in the event you use your thoughts in your choices, and thoughts solely your choices.” Since 2007, I’ve devoted my life to sharing the enjoyment of sport idea and arithmetic. MindYourDecisions now has over 1,000 free articles with no advertisements because of neighborhood help! Assist out and get early entry to posts with a pledge on Patreon.

. . . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Reply To The Viral Meme 9 + 10 = 21 Solved

(Just about all posts are transcribed shortly after I make the movies for them-please let me know if there are any typos/errors and I’ll right them, thanks).

Let’s increase either side.

(9 + 10) (base x) = 21 (base y) 9(1) + [1(x) + 0(1)] = 2(y) + 1

Now we simplify and resolve for y:

2y = 8 + x y = 4 + x/2

Since we now have quantity bases, we wish x and y to be optimistic integers. The time period x/2 requires that x be a optimistic even quantity.

Additionally since 9 is in base x, we now have x ≥ 10, because the digit 9 wouldn’t be used for a base 9 or smaller.

Thus we now have the pairs of options:

x = 10, so y = 9 x = 12, so y = 10 x = 14, so y = 12 … x, y = 4 + x/2

So at first 9 + 10 = 21 looks like a easy false equation. But when we take into consideration quantity bases, there are an infinite* variety of solutions-pretty neat!

(*countably infinite to be exact)

Sources for meme

The bottom 10 quantity system

The event and unfold of decimal numerals is an interesting historical past. I need to share a couple of fascinating components from Wikipedia:

Reality 1: the bottom 10 system was developed by Aryabhata in India, and Brahmagupta launched the image for 0. (Quoting Wikipedia) Probably the most generally used system of numerals is the Hindu-Arabic numeral system. Two Indian mathematicians are credited with growing it. Aryabhata of Kusumapura developed the place-value notation within the fifth century and a century later Brahmagupta launched the image for zero. The numeral system and the zero idea, developed by the Hindus in India, slowly unfold to different surrounding international locations resulting from their industrial and army actions with India. The Arabs adopted and modified it. Even right this moment, the Arabs name the numerals which they use “Raqam Al-Hind” or the Hindu numeral system. The Arabs translated Hindu texts on numerology and unfold them to the western world resulting from their commerce hyperlinks with them. The Western world modified them and referred to as them the Arabic numerals, as they realized them from the Arabs. Therefore the present western numeral system is the modified model of the Hindu numeral system developed in India. It additionally displays a terrific similarity to the Sanskrit-Devanagari notation, which remains to be utilized in India and neighbouring Nepal.

Reality 2: Fibonacci shared the strategy “how the Indians multiply” in 1202, but it surely took Europe a whole bunch of years to undertake the strategy. For all of the poeple that suppose base 10 is pure since we now have 10 fingers, I ponder: why did it take so lengthy for Europe to undertake a “pure” system? I don’t suppose it’s so natural-the decimal system s a revolutionary thought, and we should always give correct credit score to the Indian mathematicians who developed it.

(I’m intrigued on the similarities with a newer episode. The strategy how the Japanese multiply is a enjoyable way-not as revolutionary-to visualize multiplication and to study group idea. I really feel a bit like Fibonacci as others are very gradual to simply accept the strategy’s worth!) (Quoting Wikipedia) Within the Liber Abaci, Fibonacci says the next introducing the Modus Indorum (the strategy of the Indians), right this moment referred to as Hindu-Arabic numeral system or base-10 positional notation. It additionally launched digits that tremendously resembled the fashionable Arabic numerals.

(Quoting translated Liber Abaci on Wikipedia): “There from a fabulous instruction within the artwork of the 9 Indian figures, the introduction and information of the artwork happy me a lot above all else, and I learnt from them, whoever was realized in it, from close by Egypt, Syria, Greece, Sicily and Provence, and their varied strategies, to which areas of enterprise I travelled significantly afterwards for a lot research, and I learnt from the assembled disputations. However this, on the entire, the algorithm and even the Pythagorean arcs, I nonetheless reckoned virtually an error in comparison with the Indian methodology.

… (Quoting Wikipedia) In different phrases, in his guide he advocated the usage of the digits 0-9, and of place worth. Till this time Europe used Roman Numerals, making trendy arithmetic virtually unattainable. The guide thus made an necessary contribution to the unfold of decimal numerals. The unfold of the Hindu-Arabic system, nonetheless, as Ore writes, was “long-drawn-out”, taking many extra centuries to unfold extensively, and didn’t turn out to be full till the later a part of the 16th century, accelerating dramatically solely within the 1500s with the appearance of printing.

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