Einstein's Riddle
1. Emma lives in the first house. (#9) Emma lives next to the blue house. (#14) House #2 is blue.
2. The child in house #3 drinks milk. (#8) The child in the green house drinks lemonade. (#5) House #3 is not green.
3. The green house immediately comes before the white house. (#4) House #1 cannot be green. If house #1 were green, then house #2 would be white. However, house #2 is blue. House #2 cannot be green. It is already listed as blue. House #3 is already listed as not green. Therefore, house #4 must be green and house #5 must be white.
4. Peter lives in the red house. (#1) We already know that houses #2, #4, and #5 are blue, green, and white, so he does not live there. House #1 is Emma’s. The only one left is house #3.
5. We now know that houses #2, #3, #4, #5 are blue, red, green, and white. Therefore, house #1 is yellow.
6. The child in the yellow house likes chocolate. Therefore, Emma in house #1 likes chocolate.
7. The child who has a horse lives next to the child who likes chocolate. Emma, who likes chocolate, has only one neighbour. Therefore, the horse goes with house #2.
8. Mary has a dog. We already know the occupants of houses #1 and #3. House #2 already has a pet. Therefore, Mary lives in #4 or #5.
9. Linus drinks tea. We already know the occupants of houses #1 and #3 and the drinks of houses #3 and #4. Therefore, Linus lives in #2 or #5.
10. Anna likes cake. We already know the occupants of houses #1 and #3. Therefore, Anna lives in #2, #4, or #5.
11. The child who likes cookies has birds. Food nor pet are unknown for #3, #4, or #5.
12. The child who likes sweets lives next to the child who drinks water. Possible houses are #2, #3 or #4.
13. The child who likes gum drinks juice. Possible houses are #2 or #5.
14. The child who likes gum drinks juice. Anna and Emma’s food are known. Linus and Peter’s drink are known. Therefore, Mary likes gum and drinks juice. Juice and gum can go in #2 or #5. Mary can go in #4 or #5.#5 is the only common number. Therefore, Mary lives in house #5.
15. House #2 is the only house for which child AND drink are not known. Therefore, Linus lives in house #2.
16. Emma is the only child for whom drink is unknown. The only drink left is water.
17. Anna is the only child for whom housing is unknown. The only house open is #4.
18. Cookies and birds go together. Peter, in house #3, is the only one for whom either is unknwon.
19. Sweets is the only food left. The only open slot for food is at house #2.
20. The child who likes sweets (House #2) has a neighbour with a cat. (#10) House #1 is the only neighbor with an open pet slot.
21. Anna has fish.
Adapted from https://www.mathnasium.com/redwood-city-san-carlos-news-einsteins-riddle
Short Maths Challenges
October 18:
Warm-ups
September 7:
September 6:
September 3:
September 2:
August 31:
August 30:
Maths Challenges
September 7, Ball Problem
The bottom layer has 4 rows of 4 so 4 x 4 = 16.
The second layer has 3 rows of 3 so 3 x 3 = 9.
The third layer has 2 rows of 2 so 2 x 2 = 4.
There is 1 ball on top.
So 16 + 9 + 4 + 1 = 30. There are 30 balls.
September 6 Flower Problem
This can be solved with the equation 60 ÷3 = 20
We know the red flower is 20, so we can subtract that.
This can be solved with the equation 10 ÷2 = 5
We know the blue flower is 5, so this means 5 – 2 = 3. The flowers are 2. So each yellow flower is 1.
Now we know the values of all of the flowers: 1 + 20 + 5 = 26
September 3, Triangles Problem
There are 24 triangles:
September 2, Blocks Problem
There are four arms in the block pattern. Each arm has 15 blocks and there are another 6 blocks in the centre. So the answer is (4 x 15) + 6 = 66 blocks.
August 31, Pizza Problem
August 30, Roald Dahl Challenge 2:
The value of the characters is as follows:
The Twits (older couple) are 5,
George (boy) is 25,
Willy Wonka (man with the cane) is 50,
Enormous Crocodile is 10
and Matilda (girl) is 30.
August 27, Falling Origami Papers Problem Maths Challenge:
August 26, Roald Dahl Math Challenge 1:
Order of George’s bottles is as follows: Blue, Purple, Red, Green, Orange and Yellow.
Imposters
August 27:
The first imposter is blue (48 ÷ 8 = 6). Maybe you know this as a basic fact.
The second imposter is orange (48 x 2 = 96). One strategy for this is to remember that 50 x 2 = 100. 50 – 48 = 2. We then subtract 2 x 2 from 100: 100 – 4 = 96.
The third imposter is dark grey (88 x 2 = 176). One strategy for this is to double 80 which is 160. Then double 8 which is 16. So 160 + 16 = 176.
The fourth imposter is brown (28 x 3 = 84). You can work this out by multiplying 20 by 3 which is 60. Then 8 x 3 = 24. 60 + 24 = 84.
August 26:
The first imposter is blue (66 ÷ 3 = 21). I worked this out 30 ÷ 3 = 10, so 60 ÷ 3 = 20. Then there are two more groups of 2 which means 20 + 2 = 21.
The second imposter is green (125 x ⅕ = 125, not 125 x ⅙).
Here is some more instructions on how to multiple a whole number by a fraction:
August 25:
The first imposter is orange (126 ÷ 6 = 21). I worked this out 60 ÷ 6 = 10, so 120 ÷ 6 = 20.
Then there is one more group of 6 which means 20 + 1 = 21.
The second imposter is brown (1234 + 5678 = 6912). I used column addition to calculate this:
Every other equation was correct so there were only two imposters.
Numbers of the Day
Thursday, August 26
12
twelve;
even;
half it = 6;
double it = 24;
tens = 1, ones = 2;
10 less = 2, 10 more = 22, 100 less = -88, 100 more = 112;
add 15 = 27, subtract 7 = 5, multiply by 6 = 72, divide by 3 = 4;
12 x 10 = 120, 12 x 100 = 1200, 12 ÷ 10 = 1.2, 12 ÷ 100 = 0.12
Your number line example with 12 highlighted:
Number sentence (equation) example:
12 + 5 = 17
86
eighty-six;
even;
half it = 43;
double it = 172;
tens = 8, ones = 6;
10 less = 86, 10 more = 96, 100 less = -14, 100 more = 186;
add 15 = 101, subtract 7 = 79, multiply by 6 = 516, divide by 3 = 28 R2;
86 x 10 = 860, 86 x 100 = 8600, 86 ÷ 10 = 8.6, 86 ÷ 100 = 0.86
Your number line example with 86 highlighted:
Number sentence (equation) example:
81 + 5 = 86
972
nine-hundred and seventy-two;
even;
half it = 486;
double it = 1944;
hundreds = 9, tens = 7, ones = 2;
10 less = 962, 10 more = 982, 100 less = 872, 100 more = 1072;
add 15 = 987, subtract 7 = 965, multiply by 6 = 5,832 (I used the columns strategy), divide by 3 = 324 (I used long division);
972 x 10 = 9,720; 972 x 100 = 97,200; 972 ÷ 10 = 97.2, 972 ÷ 100 = 9.72
Your number line example with 972 highlighted:
Number sentence (equation) example:
972 + 5 = 977
5,762
five-thousand, seven-hundred and sixty-two;
even;
half it = 4,881;
double it = 11,524;
thousands = 5, hundreds = 7, tens = 6, ones = 2;
10 less = 5,752, 10 more = 5,772, 100 less = 5,662, 100 more = 5,862;
add 15 = 5,777; subtract 7 = 5,655; multiply by 6 = 34,572 (I used the columns strategy), divide by 3 = 1,920 R2 (I used long division);
5,762 x 10 = 57,620; 5,762 x 100 = 576,200; 5,762 ÷ 10 = 576.2; 5,762 ÷ 100 = 57.62
Your number line example with 5,762 highlighted:
Number sentence (equation) example:
5,762 + 5 = 5,767
Wednesday, August 25
10 (It doesn't hurt to do it again!)
ten;
even;
half it = 5;
double it = 20;
tens = 1, ones = 0;
10 less = 0, 10 more = 20, 100 less = -90, 100 more = 110;
add 15 = 25, subtract 7 = 3, multiply by 6 = 60, divide by 3 = 3 R1;
10 x 10 = 100, 10 x 100 = 1,000, 10 ÷ 10 = 1, 10 ÷ 100 = 0.1
Your number line example with 10 highlighted:
Number sentence (equation) example:
10 + 5 = 15
20
twenty;
even;
half it = 10;
double it = 40;
tens = 2, ones = 0;
10 less = 10, 10 more = 30, 100 less = -80, 100 more = 120;
add 15 = 35, subtract 7 = 13, multiply by 6 = 120, divide by 6 = 3 R2;
20 x 10 = 200, 20 x 100 = 2,000, 20 ÷ 10 = 2, 20 ÷ 100 = 0.2
Your number line example with 20 highlighted:
Number sentence (equation) example:
20 + 5 = 25
67
sixty-seven;
odd;
half it = 33.5;
double it = 134;
tens = 6, ones = 7;
10 less = 57, 10 more = 77, 100 less = -33, 100 more = 167;
add 15 = 82, subtract 7 = 60, multiply by 6 = 402, divide by 3 = 22 R1;
67 x 10 = 670, 67 x 100 = 6,700, 67 ÷ 10 = 6.7, 81 ÷ 100 = 0.67
Your number line example with 8 highlighted:
Number sentence (equation) example:
67 + 5 = 72
928
nine-hundred and twenty-eight;
even;
half it = 464;
double it = 1,856;
hundreds = 9, tens = 2, ones = 8;
10 less = 918, 10 more = 938, 100 less = 828, 100 more = 1,028;
add 15 = 942, subtract 7 = 921, multiply by 6 = 5,568 (I used the columns strategy), divide by 3 = 309 R1 (I used long division);
928 x 10 = 9,280; 928 x 100 = 92,800; 928 ÷ 10 = 92.8, 928 ÷ 100 = 9.28
Your number line example with 928 highlighted:
Number sentence (equation) example:
928 + 5 = 933
4,632
four-thousand, six-hundred and thirty-two;
even;
half it = 2,616;
double it = 9,264;
thousands = 4, hundreds = 6, tens = 3, ones = 2;
10 less = 4,622, 10 more = 4,642, 100 less = 4,532, 100 more = 4,732;
add 15 = 4,647; subtract 7 = 4,625; multiply by 6 = 27,792 (I used the columns strategy), divide by 3 = 1,544 (I used long division);
4,632 x 10 = 46,320; 4,632 x 100 = 463,200; 4,632 ÷ 10 = 463.2; 4,632 ÷ 100 = 46.32
Your number line example with 4,632 highlighted:
Number sentence (equation) example:
4,632 + 5 = 4,637
Tuesday, August 24
5
five;
odd;
half it = 2.5;
double it = 10;
tens = 0, ones = 5;
10 less = -5, 10 more = 15, 100 less = -95, 100 more = 105;
add 15 = 20, subtract 7 = -2, multiply by 6 = 30, divide by 3 = 1 R2;
5 x 10 = 50, 5 x 100 = 500, 5 ÷ 10 = 0.5, 5 ÷ 100 = 0.05
Your number line example with 5 highlighted:
Number sentence (equation) example:
5+ 5 = 10
81
eighty-one;
odd;
half it = 40.5;
double it = 162;
tens = 8, ones = 1;
10 less = 71, 10 more = 91, 100 less = -19, 100 more = 181;
add 15 = 96, subtract 7 = 74, multiply by 6 = 486, divide by 3 = 27;
81 x 10 = 810, 81 x 100 = 8100, 81 ÷ 10 = 8.1, 81 ÷ 100 = 0.81
Your number line example with 8 highlighted:
Number sentence (equation) example:
81 + 5 = 86
639
six-hundred and thirty-nine;
odd;
half it = 319.5;
double it = 1,278;
hundreds = 6, tens = 3, ones = 9;
10 less = 629, 10 more = 649, 100 less = 539, 100 more = 739;
add 15 = 654, subtract 7 = 632, multiply by 6 = 3,834 (I used the columns strategy), divide by 3 = 213 (I used long division);
639 x 10 = 6,390; 639 x 100 = 63,900; 639 ÷ 10 = 63.9, 639 ÷ 100 = 6.39
Your number line example with 639 highlighted:
Number sentence (equation) example:
639 + 5 = 644
3,490
three-thousand, four-hundred and ninety;
even;
half it = 1,745;
double it = 6,980;
thousands = 6, hundreds = 4, tens = 9, ones = 0;
10 less = 3,480, 10 more = 3,500, 100 less = 3,390, 100 more = 3,590;
add 15 = 3,505; subtract 7 = 3,483; multiply by 6 = 20,940 (I used the columns strategy), divide by 3 = 1,163 R1 (I used long division);
3,490 x 10 = 34,900; 3,490 x 100 = 349,000; 3,490 ÷ 10 = 349; 3,490 ÷ 100 = 34.9
Your number line example with 3,490 highlighted:
Number sentence (equation) example:
3,490 + 5 = 3,495
76,200
seventy-six-thousand, two-hundred;
even;
half it = 38,100;
double it = 152,400;
thousands = 76, hundreds = 2, tens = 0, ones = 0;
10 less = 76,190, 10 more = 76,210, 100 less = 76,100, 100 more = 76,300;
add 15 = 76,215; subtract 7 = 76,193; multiply by 6 = 457,200 (I used the columns strategy), divide by 3 = 25,400 (I used long division);
76,200 x 10 = 762,000; 76,200 x 100 = 7,620,000; 76,200 ÷ 10 = 7,620; 76,200 ÷ 100 = 762
Your number line example with 76,200 highlighted:
Number sentence (equation) example:
76,200 + 5 = 76,205
Monday, August 23
10
ten;
even;
half it = 5;
double it = 20;
tens = 1, ones = 0;
10 less = 0, 10 more = 20, 100 less = -90, 100 more = 110;
add 15 = 25, subtract 7 = 3, multiply by 6 = 60, divide by 3 = 3 R1;
10 x 10 = 100, 10 x 100 = 1,000, 10 ÷ 10 = 10, 10 ÷ 100 = 0.1
Your number line example with 10 highlighted:
Number sentence (equation) example:
10 + 5 = 15
67
sixty-seven;
odd;
half it = 33.5;
double it = 134;
tens = 6, ones = 7;
10 less = 57, 10 more = 77, 100 less = -33, 100 more = 167;
add 15 = 82, subtract 7 = 60, multiply by 6 = 402, divide by 3 = 22 R1;
67 x 10 = 670, 67 x 100 = 6700, 67 ÷ 10 = 6.7, 67 ÷ 100 = 0.67
Your number line example with 8 highlighted:
Number sentence (equation) example:
67 + 5 = 72
928
nine-hundred and twenty-eight;
even;
half it = 464;
double it = 1,856;
hundreds = 9, tens = 2, ones = 8;
10 less = 918, 10 more = 938, 100 less = 828, 100 more = 1,028;
add 15 = 943, subtract 7 = 921, multiply by 6 = 5,568 (I used the columns strategy), divide by 3 = 309 R1 (I used long division);
928 x 10 = 9,280, 928 x 100 = 92,800, 928 ÷ 10 = 92.8, 928 ÷ 100 = 9.28
Your number line example with 928 highlighted:
Number sentence (equation) example:
928 + 5 = 933
4,632
four-thousand, six-hundred and thirty-two;
even;
half it = 2,316;
double it = 9,264;
thousands = 4, hundreds = 6, tens = 3, ones = 2;
10 less = 4,622, 10 more = 4,642, 100 less = 4,532, 100 more = 4,732;
add 15 = 4,647, subtract 7 = 4,625, multiply by 6 = 27,792 (I used the columns strategy), divide by 3 = 1,544 (I used long division);
4,632 x 10 = 46,320, 4,632 x 100 = 463,200, 4,632 ÷ 10 = 463.2, 4,632 ÷ 100 = 46.32
Your number line example with 4,632 highlighted:
Number sentence (equation) example:
4,632 + 5 = 4,637
26 FLOWERSAA I THINK
ReplyDeletein the how many balls equation 4x4=16 3x3=9 2x2=4 1x1=1
ReplyDeletefor the flowers 1+20+5=26
ReplyDeletefor the Among us one orange and brown are the impostor 6812+22=6833
ReplyDeletegreg this is urgent the tereo maori dictonary is hacked r something
ReplyDelete