Threes And Boxes

Logic Level 1

3 □ 3 □ 3 □ 3 \large 3 \; \square \; 3 \; \square \; 3 \; \square \; 3

Fill in the boxes above with any of the four mathematical operators ( + , − , × , ÷ +, -, \times , \div ). Which of the following cannot be a resultant number?

Note : Order of operations (BODMAS) applied.

9 10 11 12

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Relevant wiki: Arithmetic Puzzles - Operator Search

3 × 3 + 3 − 3 = 9 3 \times 3+3-3=9 .

3 + 3 + 3 + 3 = 12 3+3+3+3=12 .

3 3 + 3 × 3 = 10 \dfrac 3 3 +3 \times 3=10 .

Only 11 11 cannot be a resultant number.

17 Helpful 0 Interesting 0 Brilliant 1 Confused

Can you explain why , by any combination of operators 11 can't be obtained apart from just showing that all the others can be and concluding 11 can't anyway ?

Also , considered generally which are all the numbers which can't be obtain using the 4 operators and also any sequence of some lenght of 3's anyway ?

A A - 4 years, 11 months ago

I had the exact same answer and method.

Danny Tunks - 3 years, 2 months ago

do not understand the 10 equation. 3/3 = 1 ?

Peter Haines - 4 years, 4 months ago

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3 goes into 3 precisely once.

Desmond Cann - 3 years, 11 months ago

Solution for 10 does not follow BODMAS as per question. 3/3+3x3 would be re-arranged to 3/3x3+3=6

Andrew Christofi - 3 years, 10 months ago

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Ignore brain not working this morning. Sorry

Andrew Christofi - 3 years, 10 months ago
Ervyn Manuyag
Nov 17, 2018

If you try 11 will never work

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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