Totle #5: make 12 from 8, 11, 13, 19 and 20
Saturday, October 17, 2026
Use all five numbers with + − × ÷ to make 12. Combine two at a time; every result has to be a positive whole number.
A Saturday puzzle, so level 7 of 7 (they get harder from Sunday to Saturday). There were 4 different answers. Harder than 99% of all Totle puzzles, and these five numbers can make 1,437 different totals.
About this puzzle
A Saturday puzzle, the top of the week's difficulty, and a real test: only four different answers, and it's harder than 99% of all Tōtle puzzles.
What makes it tough is the target. These five numbers can reach fifteen different targets, and 12 is the hardest of them all. Every answer needs both a subtraction and a division, so it rewards patience: try a few ideas, and keep the ones that leave you a small, friendly number.
Playing past puzzles needs a free account. They don't count toward your streak.
How people did
On the day, 3 people played it and 1 solved it (33%).
Medals among the 1 who solved it:
How to think about it
- Work backward. Ask what two numbers make 12, 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 12. It can add or subtract two numbers you've built, multiply two (12 = 2 × 6 = 3 × 4), or divide a multiple of 12 by the right number (24 ÷ 2, 36 ÷ 3, 48 ÷ 4…). Look at the numbers you have: which of those could you build?
Every answer uses − and ÷.
Hint 2: a first move
Try 11 + 13 = 24.
Hint 3: how it ends
The last move is 8 + 4 = 12. So the job is building 8 and 4 from the numbers.
Walk through it
Start from the target. 12 has lots of factors, but the numbers here are big and awkward, so the trick is to shrink them first. Subtraction is how you get small numbers out of big ones.
One easy finish is 8 + 4 = 12, since the 8 is already there. So the job becomes making a 4 from 11, 13, 19 and 20.
The 20 makes a 4 if you can divide it by 5, because 20 ÷ 5 = 4. Turn it around to check: 5 × 4 = 20. Now find a 5 in the last three numbers: 11 + 13 = 24, and 24 − 19 = 5.
Put it together: 11 + 13 = 24, 24 − 19 = 5, 20 ÷ 5 = 4, and 8 + 4 = 12.
Show an answer
- 11 + 13 = 24
- 24 − 19 = 5
Take away the 10 first (24 − 10 = 14), then the 9: 5. - 20 ÷ 5 = 4
Turn it around: 5 × 4 = 20, so 20 ÷ 5 = 4. - 8 + 4 = 12
One of 4 different answers.
Other ways to get there
- (8 × (20 − 11)) ÷ (19 − 13)
Divide down from 72 instead: 20 − 11 = 9 and 8 × 9 = 72, then 19 − 13 = 6. Finish with 72 ÷ 6 = 12, which is 60 ÷ 6 + 12 ÷ 6 = 10 + 2 = 12. - (19 + (11 × (20 − 13))) ÷ 8
The big one: 20 − 13 = 7 and 11 × 7 = 77, then 19 + 77 = 96. Since 96 ÷ 8 is 80 ÷ 8 + 16 ÷ 8 = 10 + 2 = 12, that lands it. - 19 − (11 − (20 ÷ (13 − 8)))
Make the 4 another way, with 13 − 8 = 5 and 20 ÷ 5 = 4. Then 11 − 4 = 7, and 19 − 7 = 12.