Indian | A Nice Olympiads Trick | No Calculator Allowed

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[@williamcousins3026]

from difference of squares: 9999x1111 = 10000x1111 - 1x1111 = 11110000 - 1111 = 11108889

[@tontonbeber4555]

same for me :)

[@johntsui7573]

This is indeed a better solution, or
9999x1111=(10000-1)x1111=11110000-1111=11108889

[@施銘和]

Me too

[@haroldlake1005]

same solution mine

[@fadetoblah2883]

Choosing a slightly different way to factor the initial expression, we have:
5555²-4444²
= 1111²(5²-4²)
= 1111²(25-16)
= 1111² x 9
= 1234321 x 9
= 11108889
I find that calculating 1111² first, and then multiplying by 9 is rather easier than calculating 3333², but that may just be a personal preference.

[@สุนทรราชวงศ์ศึก]

Very good

[@ahmedulmursalin8253]

Yes that's the easiest way. 11*11=121; 111*111=12321; 1111*1111= 1234321. See the pattern.

[@stuartpalmer8233]

By the time you get to 9999 x 1111 you may as well just go for the sum of four terms.

[@michallesz2]

The Pythagorean theorem that 3^2 + 4^2 = 5^2 gives us that 5555^2 - 4444^2 = 3333^2

[@GOMBE3]

exactly same until 5555^2-4444^2=9999 x 1111
after this =9999 x (1000+100+10+1)=9999000+999900+99990+9999=11108889
since no calculator allowed this is much easier to calculate, me thinks.

[@panneerselvam9223]

very long process

[@곽지은-j8j]

❤

[@gopalsinnarkar277]

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