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The Wonderful solution...
assuming a,b,c integers ... 128 + 16 + 4 ... 2^7, 2^4, 2^2 ... takes under 5 seconds
That is how I did it.
Thank you it makes me know math a little bit🥰🥰🥰
a>0 b>0 c>0 and a, b, c are integers. Therefore a
In computer science, 148 Decimal = 1001 0100 Binary7654 3210 Bit bit7 = 2^7 = 128bit4 = 2^4 = 16bit2 = 2^2 = 4a=7, b=4, c=2
For any number, not just 148 - just convert it to binary and look at the positions of 1s. That's it. Is it really Olympiad question?
4+16+128=1482^2+2^4+2^7=148
A=2B=4C=7
Solution:2^0+2²+2^5 = 37 |*4 ⟹4*2^0+4*2²+4*2^5 = 148 ⟹2²*2^0+2²*2²+2²*2^5 = 148 ⟹2²+2^4+2^7 = 148 ⟹ a = 2, b = 4, c =7.
Only one of all solutions.
2, 4 , 7
Just write 148 in binary. Each "1" is an applicable power of 2
4, 16, 128. So 2 ,4 ,7.
Without stating that a,b,c are integers, and proving uniqueness (apart from permuting numbers 2,4,7) this is not good at all.
Obvious solution: a=b=c= ln(148/3)/ln(2)
I was not aware on Olympiads in Kindergardens. Wait a bit... Wasn't this contest a kind of math Paralympiad for some mentally handicapped persons? Converting short decimal to binary really takes no longer than 5 seconds, as it was noted already.
Thank you for comment 🙏🙏
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The Wonderful solution...
assuming a,b,c integers ... 128 + 16 + 4 ... 2^7, 2^4, 2^2 ... takes under 5 seconds
That is how I did it.
Thank you it makes me know math a little bit🥰🥰🥰
a>0 b>0 c>0 and a, b, c are integers. Therefore a
In computer science,
148 Decimal =
1001 0100 Binary
7654 3210 Bit
bit7 = 2^7 = 128
bit4 = 2^4 = 16
bit2 = 2^2 = 4
a=7, b=4, c=2
For any number, not just 148 - just convert it to binary and look at the positions of 1s. That's it. Is it really Olympiad question?
4+16+128=148
2^2+2^4+2^7=148
A=2
B=4
C=7
Solution:
2^0+2²+2^5 = 37 |*4 ⟹
4*2^0+4*2²+4*2^5 = 148 ⟹
2²*2^0+2²*2²+2²*2^5 = 148 ⟹
2²+2^4+2^7 = 148 ⟹ a = 2, b = 4, c =7.
Only one of all solutions.
2, 4 , 7
Just write 148 in binary. Each "1" is an applicable power of 2
4, 16, 128.
So 2 ,4 ,7.
Without stating that a,b,c are integers, and proving uniqueness (apart from permuting numbers 2,4,7) this is not good at all.
Obvious solution: a=b=c= ln(148/3)/ln(2)
I was not aware on Olympiads in Kindergardens. Wait a bit... Wasn't this contest a kind of math Paralympiad for some mentally handicapped persons? Converting short decimal to binary really takes no longer than 5 seconds, as it was noted already.
Thank you for comment 🙏🙏