Quinary Quantity Part 1

Logic Level 2

$\large \square \ + \ \square \ - \ \square \ \times \ \square \ \div \ \square$

You are given that the numbers $1,2,3,4$ and $5$ are to be filled in the square boxes as shown above (without repetition).

By strictly applying the operations from left to right , find the maximum possible value of the resultant number. Give your answer to 3 decimal places.

See Part 2 , Part 3 and Part 4 .

The answer is 25.000.

2 solutions

Chew-Seong Cheong
Aug 11, 2015

The expression is equivalent to $S = (A+B-C)\times D \div E$ . For maximum $S$ , $D$ must be maximum, $D=5$ and $E$ , minimum, $E=1$ and $A+B-C$ the maximum with the remaining numbers, which is $3+4-2=5$ . Therefore, $S_{max} = 5\times 5 = \boxed{25}$ .

I agree that $S_{max}=\boxed{25}$ . However, I am not sure that $D=5$ is so obvious. The combination A=5, B=3, C=2, D=4, E=1 gives $S=24$ so this is extremely close. There doesn't seem to be a proof to your statement besides that it is true for this combination, unless there are some principle that I am missing. The only valid solution, I could see would to check you answer against other combinations, ie. you would need to test whether D=4 or 5.

Scott Ripperda - 5 years, 9 months ago

John Lesteя Tan
Aug 12, 2015

to maximize the value that we are getting we should divide by 1, and multiply by 5. then we add the 2 largest numbers that are left and subtract it by the last digit that is left, so we are left with 4+3 -2 x 5 / 1 = 25

Quinary Quantity Part 1

The answer is 25.000.

2 solutions

0 pending reports