Problem 2 · 2014 Math Kangaroo
Easy
Number Theory
place-value
Marie wants to put the digit 3 somewhere into the number 2014. Where must she put the 3 so that the new number (with all 5 digits) is as small as possible?
Show answer
Answer: D — between 1 and 4
Show hints
Hint 1 of 3
A number is smaller when its first (left-most) digits are smaller.
Still stuck? Show hint 2 →
Hint 2 of 3
Putting the big digit 3 near the front pushes the number up, so push the 3 as far right as you can.
Still stuck? Show hint 3 →
Hint 3 of 3
Write out each new number and read them like words to see which comes first.
Show solution
Approach: keep the small left-hand digits and push the 3 to the right
- Try the 3 in each gap: 32014, 23014, 20314, 20134, 20143.
- Reading them like a race, the one that stays smallest the longest at the front is 20134.
- So the 3 should go between the 1 and the 4.
- Answer: between 1 and 4.
Mark:
· log in to save