Geometry & Figures

Problem

Flipping or turning digits forms new digits

From the five number cards 8, 5, 9, 1, 0, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees clockwise as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.
8 5 9 1 0
Geometry
Your answer
How to solve
Strategy Make a Systematic List — To get the largest number I order the usable digits from greatest to least and place them left to right. Then I carefully diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.
1STEP 1

Build the largest three-digit number

Order the digits from greatest to least: 9, 8, 5, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, ones places: 9, then 8, then 5.

largest = 985
2STEP 2

Turn each digit 180 degrees

Turning the digits of 985 each 180 degrees: 9 becomes 6, 8 becomes 8, 5 becomes 2.

9 → 6, 8 → 8, 5 → 2
3STEP 3

Reverse the order to read the rotated number

Because the whole number is turned at once, the order reverses too. The original ones digit ends up on the left. So 985 (turned) reads as the reverse of 6, 8, 2, which is 2, 8, 6 = 286.

985 → 286 (180° turn)
4STEP 4

Subtract to find the difference

Find the difference between the original number and the rotated number.

985 - 286 = 699
Answer
Largest = 985; rotated = 286; difference = 985 - 286 = 699
985 is the biggest three-digit number from {9,8,5,1,0}, and 286 uses only valid turned digits (6,8,2). 985 - 286 = 699 is a positive three-digit difference, which is sensible since the original is larger.
Takeaway

Put the biggest digits first to make 985, then turn it upside-down (digits change AND flip order) to get 286 - easy Grade 4 place-value and subtraction!

  • Build the largest three-digit number
  • Turn each digit 180 degrees
  • Reverse the order to read the rotated number
  • Subtract to find the difference
Where next?
Another one like thissuggested

▶ Practice — 8 problems