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

## Understand the problem

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

##### Source of the problem

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

### General concepts + Number theory

##### Difficulty Level
4 out of 10

Do you really need a hint? Try it first!

DO you know how to start working backward

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

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

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

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

Praveen Kumarsays:

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

TRISHAN MONDALsays:

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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