Missing Symbols

Logic Level 1

$\large (6 \, \square \, 2) \, \square \, (3 \, \square \, 4) \, \square \, (6\, \square \, 2) = 25$

Which of these options are the appropriate mathematical operators for the five squares in the above equation?

Bonus: Can you find other operators that work?

+ \, , \, \times \, , \, + \, , \, - \, , \, \times

+ \, , \,\div \, , \,- \, , \, + \, , \, \times

+ \, , \, \div \, , \, - \, , \, - \, , \, \div

- \, , \, \times \, , \, + \, , \, - \, , \, \div

- \, , \, \div \, , \, - \, , \,+ \, , \, \div

5 solutions

Sharky Kesa
Oct 25, 2015

Testing each option, we find that only

$\large (6 - 2) \times (3 + 4) - (6 \div 2) = 25$

is true. Therefore, the answer is $-, \times, +, -, \div$ .

The next question is to determine the number of different sequences in general that satisfy the equation. So far I have that $(\div, \times, +, +, -)$ and $(-, +, +, \times, \div)$ also work.

Another follow-up question is to determine the number of distinct values that can be obtained by inserting any sequence of the $4$ standard operators into the boxes in the expression on the left-hand side of the equals sign.

Brian Charlesworth - 5 years, 7 months ago

Another solution could be ×,-,-,+,×

Aditya Sharma - 5 years, 7 months ago

Great! I think we've found all the solution sequences now.

Brian Charlesworth - 5 years, 7 months ago

I found the same.

Annu Ranjan - 5 years, 7 months ago

After one hour I decided there wasn't more, only the 4 already listed:

(6-2)x(3+4)-(6/2)=25

(6-2)+(3+4)x(6/2)=25

(6x2)-(3-4)+(6x2)=25

(6/2)x(3+4)+(6-2)=25 (this is equivalent to the second one)

I spent another ten minutes on a python script for brute forcing, and I was right. there is not an other one. :)

Laszlo Kocsis - 3 years, 1 month ago

Interesting! Can you post that question? ;)

Pi Han Goh - 5 years, 7 months ago

This problem can also be solved as: * - - +*

mohamed sultan - 5 years, 7 months ago

Brian said that 3 days ago.

Sharky Kesa - 5 years, 7 months ago

(6/2)+(3 4)+(6 2) /,+, ,+,

Spandan Pratyush - 5 years, 7 months ago

If you mean $(6 \div 2) + (3 \times 4) + (6 \times 2)$ this would give a result of $27.$

Brian Charlesworth - 5 years, 7 months ago

1111=R 2222=T 3333=E 4444=N 5555=?

Nasim Alan - 5 years, 5 months ago

Answer please

Nasim Alan - 5 years, 5 months ago

1+1+1+1=4=FOUR=R 2+2+2+2=8=EIGHT=T 3+3+3+3=12=TWELVE=E 4+4+4+4=16=SIXTEEN=N 5+5+5+5=20=TWENTY=Y The trick is to add all the digits of the given number and the result is the letter with which the number ends. Hence, 5555=Y

Samarth K - 5 years, 2 months ago

I did the same.

Benjamin Zandstra - 2 years, 4 months ago

Did anyone find this solution: $\div , \times , + , + , -$ ??

Steve Popoff - 5 years, 1 month ago

Krishna Chaitu
Nov 18, 2015

Another solution is(6×2)-(3-4)+(6*2) first of all 25 is possible with only two even and odd or 3 odd numbers

Karthi Keyan
Nov 2, 2015

another solution for this sum (6x2)-(3-4)+(6x2)=12-(-1)+12=12+1+12=25

Joshua Lowrance
Mar 1, 2018

The answer is (6 - 2) x (3 + 4) - (6 / 2) = 25.

Missing Symbols

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