Problem 10 · 2023 Math Kangaroo
Medium
Number Theory
place-value
Franziska writes down three consecutive two-digit numbers, in increasing order. Instead of the digits she uses symbols and writes □◊, ♡△, ♡□. What does Franziska’s next number look like?
Show answer
Answer: C — ♡♡
Show hints
Hint 1 of 2
The last two numbers share the same first symbol, so they have the same tens digit, while the first number's tens symbol is different.
Still stuck? Show hint 2 →
Hint 2 of 2
That means the jump from the first to the second number crosses into a new ten, so the numbers are like 19, 20, 21.
Show solution
Approach: decode each symbol by matching to three consecutive numbers
- The 2nd and 3rd numbers start with the same heart symbol, so they share a tens digit, but the 1st number starts with a different symbol, so the first step crosses a ten.
- Three consecutive numbers doing that look like 19, 20, 21: so the symbols decode to square=1, diamond=9, heart=2, triangle=0 (19=square diamond, 20=heart triangle, 21=heart square).
- Her next number is 22, which uses heart for both digits.
- So the next number is heart-heart, answer C.
Mark:
· log in to save