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Central Sum
Age 11 to 14
ShortChallenge Level 
Answer: 45 numbers
Considering different middle digits
| Middle digit | Possible numbers |
| 1 | 110 |
| 2 |
121 220 |
|
3
|
132 231 330 |
|
4
|
143 242 341 440 |
There is a pattern!
There will be 5 numbers with middle digit 5, 6 with middle digit 6, ... 9 with middle digit 9
So there are a total of 1+2+3+4+5+6+7+8+9 = 45 such numbers.
Considering different first digits
| In the 100s | In the 200s | In the 300s | In the 400s | ... | In the 900s |
|
110
121 132
143 154 165 176 187 198 |
220 231 242 253 264 275 286 297 |
330 341 352 363 374 385 396 |
440 451 462 473 484 495 |
The list is one shorter each time! |
990
|
So there are a total of 9+8+7+6+5+4+3+2+1 = 45 such numbers.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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