Problem 19 · 2012 Math Kangaroo
Stretch
Number Theory
place-value
Gregory made two 3-digit numbers from the digits 1, 2, 3, 4, 5, 6. Each digit was used only once. Afterwards he added the two numbers together. What is the largest answer he could have got?
Show answer
Answer: D — 1173
Show hints
Hint 1 of 2
To make a sum large, put the biggest digits where they count the most.
Still stuck? Show hint 2 →
Hint 2 of 2
Give the two hundreds places the largest digits, then the tens, then the units.
Show solution
Approach: place the largest digits in the highest places
- Use 6 and 5 in the hundreds places, 4 and 3 in the tens, 2 and 1 in the units.
- The two numbers add to (600 + 500) + (40 + 30) + (2 + 1).
- That is 1100 + 70 + 3 = 1173.
- The largest possible sum is 1173.
Mark:
· log in to save