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

Put the three biggest cards 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

The whole number turns at once, so the order also reverses: 6, 8, 2 read backward is 2, 8, 6 = 286.

985 → 286
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?
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