BdMO 2020 Regional Higher Secondary

For students of class 11-12 (age 16+)
saifmd
Posts:15
Joined:Wed Feb 24, 2021 12:41 am
BdMO 2020 Regional Higher Secondary

Unread post by saifmd » Thu Mar 25, 2021 2:47 am

You have 4 different two digit numbers. Among them, product of any 3 is a full square number. What can be the lowest number among these 4 numbers?

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MrCriminal
Posts:8
Joined:Wed Mar 24, 2021 6:43 pm

Re: BdMO 2020 Regional Higher Secondary

Unread post by MrCriminal » Thu Mar 25, 2021 1:50 pm

Answer is
\(16\)

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Mehrab4226
Posts:230
Joined:Sat Jan 11, 2020 1:38 pm
Location:Dhaka, Bangladesh

Re: BdMO 2020 Regional Higher Secondary

Unread post by Mehrab4226 » Thu Mar 25, 2021 7:08 pm

All four numbers must be square numbers. You can prove it using contradiction(might be a little tricky). So the smallest number of the four must be $16$.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

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