Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 22 · 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 2 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 5 (d) 4
3. 3.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
4. 4.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 252 (c) 270 (d) 261
5. 5.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 128 (c) 137 (d) 146
6. 6.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
7. 7.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 122 (c) 131 (d) 132
8. 8.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
9. 9.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 15 (c) 17 (d) 16
11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 8 (b) 6 (c) 7 (d) 5
12. 12.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 126 (d) 125
13. 13.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 45 (c) 48 (d) 15
14. 14.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 465 (c) 466 (d) 382
15. 15.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 325 (c) 288 (d) 315
16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 18 (c) 17 (d) 7
17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 6 (b) 5 (c) 4 (d) 3
18. 18.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) 72 (b) 27 (c) 8 (d) 24
19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 3 (b) 13 (c) 15 (d) 14
20. 20.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
21. 21.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
22. 22.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
23. 23.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) 15 (b) 5 (c) 18 (d) 45
24. 24.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 440 (c) 553 (d) 543
25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 4 (d) 3
26. 26.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 54 (c) 45 (d) 36
27. 27.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 117 (c) 13 (d) 39
28. 28.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 27 (c) 30 (d) 9
29. 29.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 328 (c) 327 (d) 318
30. 30.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 30 (c) 10 (d) 33
31. 31.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 388 (c) 378 (d) 387
32. 32.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) 42 (b) 45 (c) 14 (d) 126
33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 4 (d) 2
34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 21 (d) 20
35. 35.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 367 (c) 366 (d) 316
36. 36.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 615 (c) 488 (d) 625
37. 37.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) 33 (c) 36 (d) 11
38. 38.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) 21 (b) 6 (c) 54 (d) 18
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 19 (d) 17
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 9 (b) 16 (c) 19 (d) 18

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