Problems from a math competition for Russian 5th graders
- Can the digits 1 through 9 be arranged to form a number such that between all pairs of digits differing by 1 there are an odd number of other digits?
- Is there a square integer that starts with 123456789?
- A country has four types of bills, worth $1, $2, $5 and $10. Prove that if you have exactly $400 then you can pay someone else exactly $300.
- Prove that if two positive integers sum to 770, then 770 does not divide their product.
- Can the digits 1 through 9 be arranged to form a number such that between all pairs of digits differing by 1 there are an odd number of other digits?
- Is there a square integer that starts with 123456789?
- A country has four types of bills, worth $1, $2, $5 and $10. Prove that if you have exactly $400 then you can pay someone else exactly $300.
- Prove that if two positive integers sum to 770, then 770 does not divide their product.
