Currency notes - Part 1

Number Theory Level 3

At an Automated Teller Machine (ATM), notes of denominations 100, 500 and 1000 are dispensed. In order to prevent fraud, you can withdraw a maximum of 40 notes in one transaction.

What is the smallest multiple of 100 that the ATM is unable to release in one transaction?

Image credit: Wikipedia George Grinsted
37400 34700 41000 36900

Unnikrishnan V by Unnikrishnan V , 47, India

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3 solutions

Sandeep Naik
Apr 15, 2014

For 36900 one needs '36' 1000 denomination notes, '1' 500 denomination note and '4' 100 denomination notes. But then the total number of notes will be 41 which the ATM cannot handle (transaction is not possible)...and 36900 being the smallest multiple of 100 in the given options...that is the answer.

12 Helpful 0 Interesting 0 Brilliant 0 Confused

For 36900 one needs '36' 1000 denomination notes, '1' 500 denomination note and '4' 100 denomination notes. But then the total number of notes will be 41 which the ATM cannot handle (transaction is not possible)...and 36900 being the smallest multiple of 100 in the given options...that is the answer.

Pankaj Ahuja - 7 years, 1 month ago

It is obvious that 36900 is not possible (see solutions below). However, that only shows 36900 is the minimum number that is not possible among the choices given. It is important to show that every other multiple below 36900 is possible.

It is easy to see that you need at most 5 notes to create a multiple of 100 between 100 and 900. With rest 35 notes available you can create multiples of 1000 between 1000 and 35000. Hence, with forty notes, we can easily create any multiple of 100 between 100 and 35900.

Extending a similar argument, you can show that it is possible to create any multiple of 100 between 36000 and 36800.

For sake of completeness, the following is the complete list of multiples of 100 that are not possible: 36900, 37400, 37800, 37900, 38300, 38400,38700,38800,38900,39200,39300,39400,39600,39700,39800,39900, and any thing more than 40000.

10 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you. That cleared it up :)

Kp Govind - 7 years, 1 month ago
Harikesh Yadav
Apr 15, 2014

36+1+4=41(smallest amount=36900)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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