The figure shows that a 10 x 10 table is filled with repeating numbers on its diagonal. Find the total sum of the table’s numbers in your head.
Grid – 10×10
Solution: The total of all the numbers in the table is 1000.
Let’s separate out the numbers by the number of their occurrences –
- 1 time -> 19 and 1
- 2 times -> 2 and 18
- 3 times -> 3 and 17
- 4 times -> 4 and 16
- 5 times -> 5 and 15
- 6 times -> 6 and 14
- 7 times -> 7 and 13
- 8 times -> 8 and 14
- 9 times -> 9 and 11
- 10 times -> 10 and 10
Conclusion: 1 &19 add up to 20. Both are displayed once. 2 &18 add up to 20. Both are shown twice. 3 & 17 add up to 20. Both are displayed thrice. 4 & 16 add up to 20. Both are displayed four times. 5 & 15 add up to 20. Both are shown five times. 6 & 14 add up to 20. Both are displayed six times. 7 & 13 add up to 20. Both are displayed seven times. 8 & 12 add up to 20. Both are shown eight times. 9 & 11 add up to 20. Both are displayed nine times. 10 is shown 10 times. Adding it all, we get a sum of 1000.