what numbers have a remainder of 1 when they are divided by 2 or by 5?
when it is put into bunches of 3
there is 1 left over
when it is put into bunches of 5
there is 2 left over
when it is put into bunches of 7
there is 3 left over?
there is a similar problem that was brought to my attention by David Wells, seemingly offered by Sun Tsu-Ching who worked on the Chinese remainder theorem (around the 4th century CE - I like the idea of students working on similar problems to their ancient ancestors):
- when you divide a number by 3, the remainder is 2
- when you divide it by 5, the remainder is 3
- when you divide it by 7, the remainder is 2