Roads
What highway number matches either clue?
A historic U.S. highway linking Chicago and Los Angeles.
OR
The value of:
1 + 2 + 3 + ... + 11
66 (Route 66)
A rhombus has perimeter 52 meters and one diagonal measuring 24 meters. Find its area.
120 m²
A chess team has two boys and three girls. For a photograph, all five sit in one row, with a boy at each end. How many seating arrangements are possible?
12, 2!*3!
Yunji adds the integers 1 through 9 but accidentally skips one number. Her result is a perfect square. Which number did she skip?
9
As a boy, Cheenu ran 15 miles in 3 hours 30 minutes. As an older man, he walks 10 miles in 4 hours. How many additional minutes does each mile take him now?
10 minutes
What highway number matches either clue?
An interstate running from Miami, Florida, to Maine.
The value of:
4 * 4! - (4 * 4 * 4 * 4) / (4^4)
95 (interstate 95)
A 4 × 4 × 4 cube-shaped cake is frosted on its top and four sides, but not its bottom. It is sliced into 64 unit cubes. How many pieces have frosting on exactly two faces?
20
Four different marbles—Aggie, Bumblebee, Steelie, and Tiger—are displayed in a row. How many arrangements keep Steelie and Tiger apart?
12, 4!-2*3!
Two positive integers add to 28. One is k more than twice the other. How many different positive integer values of k are possible?
9
SalLy sells sEashelLs bY thE seaSHore, bUt SaW sOmeOne wHo wanTEd sMOres.
How many of the character "s" is in the sentence?
9
Speaking of counting letters, Large Language Models have a very hard time counting letters. Try asking one "How many r's are in strawberry?" :/
What highway number matches either clue?
An interstate running from New York City to the Canadian border near Montreal.
OR
The value of:
2^6 + 2^5 - 2^4 + 2^3 - 2^2 + 2^1 + 2^0
87 (Interstate 87)
A 12-foot by 16-foot room gets a border of 1-foot square tiles, one tile wide. The remaining interior uses 2-foot square tiles. How many tiles are needed altogether?
87
Six students randomly occupy two rows of three seats. What is the probability that Abby and Bridget sit immediately next to each other horizontally or vertically? Diagonal neighbors do not count.
7/15
The five-digit number 2018U is divisible by 9. What remainder does it leave when divided by 8?
3. U=7, 20187 = 8 × 2523 + 3
In the MCU, there are six infinity stones. How many total letters were used?
For example, "korg" and "thor" use a total of 6 letters (t, h, o, r, k, g)
16
What highway number matches either clue?
An interstate running from Michigan to Montana through Milwaukee.
OR
The minimum number of passengers that requires four buses if each bus holds at most 31 passengers.
94 (Interstate 94)
The midpoints of a rectangle’s sides are (−3, 0), (2, 0), (5, 4), and (0, 4). What is the rectangle’s area?
40 Square Units
Divide nine cards numbered 1 through 9 into three groups of three. Each group must have the same sum. How many different groupings exist? The groups are unlabeled.
2. The groupings are {1,5,9}, {2,6,7}, {3,4,8}; and {1,6,8}, {2,4,9}, {3,5,7}.
For even n, define n!! = 2 × 4 × 6 × … × n. What is the units digit of 2!! + 4!! + 6!! + … + 2022!!?
2. The first 4 add to 442, the rest end in 0.
Greta Grasshopper can jump five lily-pad positions right or three left. What is the fewest jumps needed to finish 2023 positions to the right of where she started?
411 jumps: 407 rightward and 4 leftward, giving
407 * 5 - 4 * 3 = 2035 - 12 = 2023.
What highway number matches either clue?
A West Coast interstate running from the U.S.–Mexico border to the U.S.–Canada border.
OR
The number of two-digit Fibonacci numbers.
An equilateral triangle with side length 216 is inscribed in a circle, with radius w√ (3)
Find W.
72
Five distinct awards are distributed among three students. Every student must receive at least one award. How many distributions are possible?
150, from 3⁵ − 3 × 2⁵ + 3.
A sequence contains positive integers. Every term after the second equals the product of the previous two. If the sixth term is 4000, what is the first term?
5. If the first terms are a and b, the sixth is a³b⁵. Factoring 4000 gives a = 5, b = 2.
ESTIMATION GAME:
How many hot dogs does Costco sell in a year?
500 Thousand
5 Million
50 Million
250 Million
500 Million
~250 Million Hot dogs
Hot dawg!