# Number Theory - Working backward - C.M.I UG -2019

## Understand the problem

[/et_pb_text][et_pb_text _builder_version="3.27.4" text_font="Raleway||||||||" background_color="#f4f4f4" custom_margin="10px||10px" custom_padding="10px|20px|10px|20px" box_shadow_style="preset2"]  If there exists a calculator with 12 buttons, 10 being the buttons for the digits and A and B being two buttons being processes where if n is displayed on the calculator if A is pressed it increases the displayed number by 1 and if B is pressed it multiplies n by 2 hence 2n. Hence find the minimum number of moves to get 260 from 1

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C.M.I (Chennai mathematical institute ) U.G- 2019 entrance

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### General concepts + Number theory

[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="3.22.7" open="off"]4 out of 10

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Challenges and Thrills of Pre-College Mathematics by University Press[/et_pb_accordion_item][/et_pb_accordion][et_pb_tabs active_tab_background_color="#0c71c3" inactive_tab_background_color="#000000" _builder_version="3.22.7" tab_text_color="#ffffff" tab_font="||||||||" background_color="#ffffff"][et_pb_tab title="Hint 0" _builder_version="3.22.4"]Do you really need a hint? Try it first!

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DO you know how to start working backward

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working backward means that when you press A is makes -1 from the result  and pressing B you can divide 2

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strategies are like this , divide the no. as many step you can , when the result it not divisible by 2 just -1

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$260\rightarrow130\rightarrow65\rightarrow64\rightarrow32\rightarrow16\rightarrow8\rightarrow4\rightarrow2\rightarrow1$

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## Similar Problem

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### 2 comments on “Number Theory - Working backward - C.M.I UG -2019”

1. Praveen Kumar says:

1,2,4,8,16,32,64,65,130,260
therefore just 9 moves

2. TRISHAN MONDAL says:

here it is said to find minimum ways

let 1 was typed now i press another digit key 3 now i again pressed a digit 0 then i press B

hence it proceed that 1-13-130-260 hence it is only 3 moves .........

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