Patterns and rules · Usually met around P4
Two unknowns
List them in order: one up by 1, the other down by 1.
How to do it
Method
List them in order: one up by 1, the other down by 1
△ + ○ = 10 (1 to 9): 1 and 9 … 9 and 1, 9 pairs
Another way
Guess and adjust
Sum 10, difference 4: 5 and 5 → 6 and 4 → 7 and 3
In full
△ + ○ = 10 has more than one answer: 3 and 7 work, and so do 4 and 6. To find them all, make an orderly list: start △ at the smallest number and go up by 1 each time, so ○ goes down by 1, until you can't go on. That way none is missed or counted twice. First check which numbers are allowed: whether 0 counts, and the largest. If there is a second fact (say △ is 4 more than ○), find the one pair in the list that fits both. Or guess a pair and adjust: if the difference is too big, take 1 from the bigger number and give it to the smaller.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
△ + ○ = 13. When △ = 10, ○ = □; when △ = 3, ○ = □.
Fill in each box
Show the answer and working
Answer: 3，10
○ is 13 take away △: 13 − 10 = 3, 13 − 3 = 10. A different △ gives a different ○.
Example 2
△ + ○ = 15, where △ and ○ are whole numbers from 1 to 9 (△ = 1, ○ = 2 and △ = 2, ○ = 1 count as two pairs). How many pairs are there?
Show the answer and working
Answer: 4
List them in order: △ is at least 6 and at most 9, each with one ○, so 4 pairs.
Example 3
Which pair fits △ − ○ = 9?
- A. △ = 13, ○ = 4
- B. △ = 6, ○ = 3
- C. △ = 4, ○ = 13
- D. △ = 14, ○ = 4
Choose the right answer
Show the answer and working
Answer: A. △ = 13, ○ = 4
13 − 4 = 9: only this pair fits.
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