Copyright © University of Cambridge. All rights reserved.

'Central Sum' printed from https://nrich.maths.org/

Show menu

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.