Casual Number Puzzles for MathsConf18

1. #mathsconf18 Maths Spa 2

2. Casual number puzzles

3. Casual Number Puzzles • These can be useful as fillers / ways to practice basic concepts that are a little more interesting than drill exercises. • Shikaku • Daily Set Puzzles • Area Puzzles

4. Shikaku

5. Shikaku

6. Shikaku

7. SET

8. Daily Set Puzzle {6 sets}

9. Daily Set Puzzle

10. Area Puzzles

11. Area Puzzles x2 x(15/13)

15. 24 25 If both 25, then ? = 6

16. 21 / (63/12) = 4

17. …so (34/6) *3 = 17 …so 9-6 = 3 …so 48/8 = 6 34

18. Sequence Puzzles

19. Versatility • As with all topics in maths, the key to smart puzzles is innovation and good subject knowledge. What follows are some pretty advanced and difficult questions on what can sometimes feel like a relatively easy topic. • Smarter questions test knowledge depth

20. Sequence Problems: • The first term of a sequence is 96, every term thereafter is 2.5x the previous term. What is the last integer in the sequence? • What do I do with the 4th difference of a quartic sequence to find the nth term? An irregular convex polygon: • The interior angles of an irregular convex • Polygon follow the sequence 160, 155, 150, 145 etc. • How many sides does it have?

21. Sequence Problems: • The first term of a sequence is 96, every term thereafter is 2.5x the previous term. What is the last integer in the sequence? 9375 • What do I do with the 4th difference of a quartic sequence to find the nth term?24 An irregular convex polygon: • The interior angles of an irregular convex • Polygon follow the sequence 160, 155, 150, 145 etc. • How many sides does it have? 9

22. Proof • The sum of consecutive odd numbers starting at 1 is always… • The sum of any 3 consecutive odd numbers is always… • AB-BA is always a multiple of … • If the sum of digits of any number are a multiple of 9, then the number is divisible exactly by 9. • The product of 4 consecutive numbers + 1 is always…

23. (n-1)+n+(n+1) = 3n • AB-BA=(10A+B)-(10B+A) = 9A-9B = 9(A-B) • 1000a + 100b + 10c + d = 999a + 99b + 9c + a + b + c + d

24. The product of 4 consecutive numbers + 1 is always a square number -> the product of 4 consecutive numbers is 1 less than a square number • n(n+1)(n+2)(n+3) = n(n+3)(n+1)(n+2) = (n2+3n)(n2+3n+2) Or a(a+2) where a = n2+3n a(a+2) = (a+1)2 - 1

34. Geometry Tip Sheet…

43. 8/27

44. Small semicircle is quarter of the area of big one • So is each 45° sector. • This means the white bit of the small semicircle plus either pink bit is 1/4 the area of the big one. So, ...

47. {unit squares}