Q1.
Complete Table 2 with 5-digit numbers whose digits are ‘1’, ‘0’, ‘6’, ‘3’, and ‘9’ in some order. Only a coloured cell should have a number greater than all its neighbours. Once you have filled the table above, put commas appropriately after the thousands digit.
Answer
Every number must use the digits 1, 0, 6, 3, 9 exactly once. The five coloured cells are the 1st and 4th of row 1, the 3rd of row 2, and the 2nd and 4th of row 4. Here is one correct filling (the numbers already printed in the book are shown in grey):
| 96,310 | 96,301 | 36,109 | 39,160 |
| 96,103 | 13,609 | 60,319 | 19,306 |
| 13,906 | 10,396 | 60,193 | 60,931 |
| 10,369 | 10,963 | 10,936 | 69,031 |
Check the five coloured cells (orange):
96,310 > 96,301 and 96,103 ✓ (it is the biggest number you can make with these digits)
39,160 > 36,109 and 19,306 ✓
60,319 > 36,109, 13,609, 19,306 and 60,193 ✓
10,963 > 10,396, 10,369 and 10,936 ✓
69,031 > 60,931 and 10,936 ✓
39,160 > 36,109 and 19,306 ✓
60,319 > 36,109, 13,609, 19,306 and 60,193 ✓
10,963 > 10,396, 10,369 and 10,936 ✓
69,031 > 60,931 and 10,936 ✓
No other cell beats all its neighbours — for example 96,103 loses to 96,310 above it, and 60,193 loses to 60,319 above it.
Tip: in the Indian system the comma goes after the thousands digit, so 96310 is written 96,310 and read as “ninety-six thousand three hundred ten”.