Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 283 · 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.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 23 (c) 69 (d) 207
2. 2.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
3. 3.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 153 (c) 17 (d) 54
4. 4.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) 18 (c) 5 (d) 15
5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 21 (d) 9
6. 6.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
7. 7.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 58 (c) 49 (d) 40
8. 8.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 16 (d) 14
10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 3 (b) 4 (c) 2 (d) 5
11. 11.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 24 (c) 7 (d) 63
12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 17 (d) 18
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 6 (d) 16
14. 14.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 235 (c) 234 (d) 225
15. 15.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 381 (c) 332 (d) 391
16. 16.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) 198 (d) 22
17. 17.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 48 (c) 38 (d) 47
18. 18.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
19. 19.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 553 (d) 552
20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 6 (c) 7 (d) 5
21. 21.The numbers 17 to 25 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) 189 (c) 21 (d) 63
22. 22.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 156 (c) 166 (d) 165
23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 18 (d) 17
24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 6 (d) 7
25. 25.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) 48 (c) 16 (d) 51
26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 18 (c) 16 (d) 17
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 19 (d) 9
28. 28.The numbers 10 to 18 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) 14 (c) 42 (d) 126
29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 4 (b) 16 (c) 14 (d) 15
30. 30.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) 18 (b) 54 (c) 57 (d) 162
31. 31.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 1 (b) 2 (c) 4 (d) 3
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 19 (d) 21
34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 13 (d) 14
35. 35.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 601 (c) 472 (d) 591
36. 36.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 131 (c) 140 (d) 122
37. 37.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 228 (c) 219 (d) 224
38. 38.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 640 (c) 498 (d) 630
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 8 (d) 19
40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 14 (d) 4

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