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?

1 Answer
Apr 4, 2017

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 3or10, or as the sum of a multiple of 10 and a multiple of3.

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

What about the numbers less than 20 that cannot be formed with 3and10?

19=10+9=10+3×3
18=6×3
17=???????????????