Totle #3: make 17 from 3, 9, 12, 14 and 20
Thursday, October 15, 2026
Use all five numbers with + − × ÷ to make 17. Combine two at a time; every result has to be a positive whole number.
A Thursday puzzle, so level 5 of 7 (they get harder from Sunday to Saturday). There were 10 different answers. Harder than 86% of all Totle puzzles, and these five numbers can make 1,272 different totals.
About this puzzle
A Thursday puzzle, and the week is starting to bite: it's harder than most Tōtle puzzles so far, with just ten different answers to find.
The target is 17, a prime, so there's no tidy multiplication waiting at the end. Every answer needs a subtraction somewhere, and the 12 and 14 sitting close together are worth a long look.
Playing past puzzles needs a free account. They don't count toward your streak.
How people did
On the day, 14 people played it and 7 solved it (50%).
Medals among the 7 who solved it:
How to think about it
- Work backward. Ask what two numbers make 17, then whether you can build them from what you have.
- Find the even splits. Division has to come out even, so spot the pairs that divide cleanly early.
- Make a 1 to use up a spare number. Two numbers one apart subtract to 1, and × 1 or ÷ 1 changes nothing.
- Break big numbers into tens. 7 × 16 is 70 + 42; 91 ÷ 7 is 70 ÷ 7 + 21 ÷ 7, or 10 + 3.
Hints and an answer
Tap one at a time to open it.
Hint 1: think about the target
The last move makes 17. It can add or subtract two numbers you've built, multiply two (17 is prime, so only 1 × 17), or divide a multiple of 17 by the right number (34 ÷ 2, 51 ÷ 3, 68 ÷ 4…). Look at the numbers you have: which of those could you build?
Every answer uses −.
Hint 2: a first move
Try 3 × 9 = 27.
Hint 3: how it ends
The last move is 27 − 10 = 17. So the job is building 27 and 10 from the numbers.
Walk through it
Start from the target. 17 is prime, so the last move is probably a + or a −. That means looking for a number near 17 you can reach, then closing the gap.
Look at what the numbers can do in one step. 3 × 9 = 27 is 10 more than 17, and 20 is 3 more. Either one gives you a clear job: make 10, or make 3, from what's left.
Try the 27. You need a 10 from 12, 14 and 20. The 12 and 14 are close, so 14 − 12 = 2, and 20 ÷ 2 = 10. To check the division, turn it around: 2 × 10 = 20.
Put it together: 3 × 9 = 27, 14 − 12 = 2, 20 ÷ 2 = 10, and 27 − 10 = 17.
Show an answer
- 3 × 9 = 27
- 14 − 12 = 2
- 20 ÷ 2 = 10
Turn it around: 2 × 10 = 20, so 20 ÷ 2 = 10. - 27 − 10 = 17
One of 10 different answers.
Other ways to get there
- (3 + 14) × ((9 + 12) − 20)
Make 17 straight away with 3 + 14 = 17, then use up the rest as a 1: 9 + 12 = 21 and 21 − 20 = 1. Finish with 17 × 1 = 17. - (20 + 14) ÷ (12 ÷ (9 − 3))
Aim for 34, the double of 17: 20 + 14 = 34. Then make a 2 with 9 − 3 = 6 and 12 ÷ 6 = 2, and halve it: 34 ÷ 2 = 17. - (12 + 20) − (3 × (14 − 9))
Go over and come back: 12 + 20 = 32, and 14 − 9 = 5 with 3 × 5 = 15. Then 32 − 15 = 17.