Missing digits

In your book, Maths Mela (Chapter 7), there is a puzzle called The Missing Digits. Some digits in a sum are hidden, and we find them. Take _6 + 1_ = 50. Start with the ones: 6 + something must end in 0, so it is 6 + 4 = 10. That gives 1 ten to regroup. Tens: something + 1 + 1 = 5, so the missing tens digit is 3. The sum is 36 + 14 = 50.

Another one: 3_2 + _88 = 890. Ones: 2 + 8 = 10, write 0 and regroup 1 ten. Tens: the missing digit + 8 + 1 must end in 9, so the missing digit is 0. Hundreds: 3 + something = 8, so it is 5. The sum is 302 + 588 = 890. And 65 − __ = 25 means 'what do we take from 65 to leave 25?' It is 40.

The book also has a Number Pair Hunt. The grid has 4 rows. Row 1: 35, 100, 179, 68. Row 2: 111, 185, 143, 54. Row 3: 300, 48, 225, 190. Row 4: 54, 321, 63, 167. Two numbers that are next to each other, across or down, make a number pair. So 35 and 100 are a pair, and 35 and 111 (just below it) are a pair.

Which pair has the greatest sum? Look for two big neighbours: 225 and 190 give 415. The smallest sum is 68 + 54 = 122 (68 is just above 54). The greatest difference is 321 − 48 = 273 (48 is just above 321). The smallest difference is 68 − 54 = 14. You do not need to check every pair: think about which neighbours are big, small, far apart or close together.