Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 361 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 3 (d) 2
2. 2.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
3. 3.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 69 (c) 22 (d) 198
4. 4.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 228 (c) 237 (d) 230
5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
6. 6.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 94 (c) 93 (d) 102
7. 7.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 6 (d) 18
8. 8.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 27 (c) 24 (d) 72
9. 9.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 70 (c) 79 (d) 88
10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 20 (d) 8
11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 6 (d) 3
12. 12.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 5 (c) 18 (d) 15
13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 18 (b) 20 (c) 19 (d) 9
14. 14.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
15. 15.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 180 (c) 20 (d) 63
16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
17. 17.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 314 (c) 363 (d) 354
18. 18.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 494 (c) 633 (d) 624
19. 19.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
20. 20.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 163 (d) 172
21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 7 (b) 5 (c) 6 (d) 8
22. 22.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 146 (c) 155 (d) 156
23. 23.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 386 (c) 471 (d) 462
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 6 (b) 8 (c) 7 (d) 5
25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 13 (c) 4 (d) 14
26. 26.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 38 (d) 47
27. 27.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 19 (c) 57 (d) 60
28. 28.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
29. 29.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
30. 30.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 564 (c) 565 (d) 555
31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 17 (d) 6
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 14 (d) 4
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
34. 34.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 152 (c) 162 (d) 161
35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 2 (d) 4
36. 36.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 51 (c) 16 (d) 48
37. 37.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 57 (c) 162 (d) 18
38. 38.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 99 (c) 108 (d) 100
39. 39.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 250 (c) 240 (d) 249
40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 1 (d) 3

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad