Number Card Puzzles Practice Test Worksheets
Number card puzzles ask you to arrange four digits into two 2-digit numbers that make a target sum. The trick is to use place value: tens digits do most of the work, and units digits fine-tune the total.
For students who can add two-digit numbers, but need practice using place value to test possible card arrangements.
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What Do Number Card Puzzles Questions Look Like?
Number card questions ask you to select digit cards and arrange them into two-digit numbers that add up to a given target. Success depends on balancing tens and units digits strategically. Here is a worked example.
Build the Target from Place Value
Question: Use cards 8, 4, 7, and 5 to make two 2-digit numbers with a sum of 105.
Worked Method
Step 1: The target ends in 5, so the two units digits must add to 5 or 15. No pair of these cards adds to 5; only 8 + 7 adds to 15.
Step 2: That leaves 5 and 4 as tens digits, contributing 50 + 40 = 90. Add the units total of 15 to get 105, so arrange the cards as 58 + 47.
Step 3: Check the sum: 58 + 47 = 105.
Tip: Each tens digit contributes ten times its value; each units digit contributes its face value.
Rules to Help You Solve Number Card Puzzles Questions
To solve number card puzzles like the example above, work methodically with place values rather than random guessing. Keep these four rules in mind:
🔢 Rule 1: Use all four cards once
No digit can be repeated or ignored. The final answer must use every card exactly one time.
Example: Cards 8, 4, 7, 5 can make 58 + 47.
🏗️ Rule 2: Tens digits set the rough size
The two tens digits decide the main size of the sum. Choose them so their tens total is close to the target.
Example: Tens digits 5 and 4 contribute exactly 90 before the units are added.
🎯 Rule 3: Units digits finish the target
After choosing tens digits, check whether the two remaining unit digits complete the exact total.
Example: 58 + 47 = 105 because 8 + 7 gives the needed units and carry.
🔁 Rule 4: Swapping units preserves the total
Swapping the two units digits in a valid solution always gives another valid solution here. Their sum stays the same, and the tens digits do not change.
Example: 58 + 47 = 105 and 57 + 48 = 105.
Two More Worked Examples
Here are two more examples showing how to use units swaps and avoid picking tens digits that are too large.
Use the Units Swap
Question: Cards 9, 4, 3, and 8 must make a sum of 87.
Worked Method
Step 1: The target ends in 7, so the units must add to 7 or 17. The possible pairs are 4 + 3 = 7 and 8 + 9 = 17.
Step 2: If 4 and 3 are units, the remaining tens give 80 + 90 + 7 = 177, which fails. Use 8 and 9 as units instead: the remaining tens give 40 + 30 + 17 = 87.
Step 3: Two answers work: 48 + 39 or 49 + 38.
Tip: Once an arrangement works, swapping its units digits always preserves the total: 8 + 9 and 9 + 8 both equal 17.
Do Not Choose Tens Digits That Are Too Large
Question: Cards 9, 2, 8, and 4 must make a sum of 77.
Worked Method
Step 1: Start by adding the face values of all four cards: 9 + 2 + 8 + 4 = 23.
Step 2: Putting a card in a tens position makes its contribution ten times as large. Its face value is already included in 23, so this adds nine times its value. For example, putting 4 in tens adds 40 − 4 = 36 = 9 × 4.
Step 3: We need to add 77 − 23 = 54. The two tens digits must therefore sum to 54 ÷ 9 = 6. Only 2 and 4 make 6 from these cards.
Step 4: Use 2 and 4 as tens and 8 and 9 as units: 48 + 29 = 77. Swapping units gives 49 + 28 = 77.
Tip: Calculate the required tens-digit sum as (target − sum of all four digits) ÷ 9, then find a pair of cards with that sum. This tells you exactly which digits belong in tens.
