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## Question

An elderly professor arrives home without his key and realizes he must use the keypad he had installed for this reason.

He is however not only habitually forgetful, but also extremely insecure. As such he has set up that each time he enters his house via the keypad (which he only does when he forgets his key) the combination will be changed before the next use.

The number changes as follows:

The first number is doubled and the 1's place of the double digit becomes the new first number.

The tens place is carried and added to the second number. Again the 1's digit of this number is the new second number.

The tens digit is added to the fourth number and the 1's digit of the this number is the new 4th number.

The third number is increased by 3 (if it goes over 10 the ten's digit is discarded).

Question 1:

A. If the code is 0123, what was it last time the professor forgot his key?

B. How many times has he forgotten his key?

Questions 2:

A. If the code is started with 1111 and it ended in 1 last time but now ends in 2, how many times has the professor forgotten his key.

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i think imm missing something

if its is odd it has to have started that way

so

1. just programed

2.0

3.1

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i think imm missing something

if its is odd it has to have started that way

so

1. just programed

2.0

3.1

My clues were probably misleading, they start in order from left to right. So my first clue refers to the furthest left digit (thousands place) and the last one refers to the furthest right digit (ones place).

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second swat

1. i think it could be 5093 or 0193

if it was 5093 he had never forgoten his key if it was 0193 all you know is the last key was 0163 or 5063

which would mean if it was 5063 it was the first miss

if it was 0163 then it could have been (and on and on)

3. if it started with 1111 then every 4 turns the second position goes up two so in 20 it goes up 10

so 20 misses or

21 codes

however i think it is possible that it could have been any multiple of 200 misses or

multiple of 200 +1 codes

i kept saying misses instead of forgotten keys

hope i understood the process right

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second swat

1. i think it could be 5093 or 0193

if it was 5093 he had never forgoten his key if it was 0193 all you know is the last key was 0163 or 5063

which would mean if it was 5063 it was the first miss

if it was 0163 then it could have been (and on and on)

3. if it started with 1111 then every 4 turns the second position goes up two so in 20 it goes up 10

so 20 misses or

21 codes

however i think it is possible that it could have been any multiple of 200 misses or

multiple of 200 +1 codes

i kept saying misses instead of forgotten keys

hope i understood the process right

Correct!

I actually missed the second solution of it starting with a 0, which of course tells you nothing about how many times the code has changed.

I know it's a fairly simple problem, but thanks for humoring me and working with the poor syntax .

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yah good puzzle man I had fun with it

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a)0193

20 times

give a hint for "b" in question 1.

i dont think it is a complete question

Edited by rohit_bd

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