Question

In Cuba there are banknotes with values of 3, 10 and 20 pesos. Using only these banknotes, what is the largest amount that can not be formed?

Answer 1

`17`

Explanation:

What an intriguing question!

Note that the first 10 multiples of 3 end on every possible digit from 0 to 9.

`3," "6," "9," "12," "15," "18," "21," "24," "27," "30`

Arranged so the units are in order from `0` to `9:`

`30," "21," "12," "3," "24," "15," "6," "27," "18," "9`

Every number from `20` upwards can be written either as a multiple of `3 or 10`, or as the sum of a multiple of `10` and a multiple of`3`.

`20 = 10+10`
`21 = 7 xx3`
`22 = 10+12 = 10 +4 xx3`
`23 = 10+3`
`25 = 10+15 = 10+5xx3`
`26 = 20+2xx3`
`28 = 10 +18 = 10 +6xx3`
`29 = 10+3xx3`
`31 = 10 +21 = 10 +7xx3`
`32 = 20+12 = 20+4xx3` etc.....

What about the numbers less than 20 that cannot be formed with `3 and 10?`

`19 = 10+9 = 10+3xx3`
`18 = 6xx3`
`17 = ???????????????`