Ones And Zeroes

Logic Level 1

10 □ 10 □ 10 □ 10 = 101 \large 10\; \Box\; 10\; \Box\; 10\; \Box\; 10=101

What series of signs will make the equation above true?

Obey the order of operations .

− − − - - - + − × + - \times × + ÷ \times + \div ÷ + − \div + -

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Alex Wang by alex wang , 19, USA

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1 solution

Sam Bealing
Jul 5, 2016

Relevant wiki: Arithmetic Puzzles - Operator Search

We need to use order of operations ( BODMAS ) to solve this problem. Checking the options we see:

10 × 10 + 10 ÷ 10 = 101 10 \boxed{\times} 10 \boxed{+} 10 \boxed{÷} 10=101

× , + , ÷ \boxed{\boxed{\times, +, ÷}}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

10x10=100 100+10=110 110÷10=11, Not 101

Javier Sanchez - 4 years, 10 months ago

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You must use BODMAS which tells you that you do D ivision before A ddition so:

10 × 10 + 10 ÷ 10 = ( 10 × 10 ) + 10 ÷ 10 As we do multiplication first = 100 + 10 ÷ 10 = 100 + ( 10 ÷ 10 ) Division comes next = 100 + 1 And finally addition = 101 As we wanted \begin{aligned} & 10 \times 10 + 10 \div 10 \\ = & (10 \times 10) + 10 \div 10 \quad \quad \color{#3D99F6}{\text{As we do multiplication first}} \\ = & 100 + 10 \div 10 \\ = & 100 + (10 \div 10) \quad \quad \color{#3D99F6}{\text{Division comes next}} \\ = & 100 + 1 \quad \quad \color{#3D99F6}{\text{And finally addition}} \\ = & \boxed{\boxed{101}} \quad \quad \color{#3D99F6}{\text{As we wanted}} \end{aligned}

Sam Bealing - 4 years, 9 months ago

You must use the BODMAS Rule to get the right solution .

Satwik Murarka - 4 years, 10 months ago

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