USING ONLY THE NUMBER FOUR, PLACE TEN MONEY AMOUNTS IN THE TEN BLOCKS OF THIS PYRAMID TO TOTAL $10,000
what pyramid?
Also need help with this one.
The pyramid had one block at the top, underneath two, underneath that three, and underneath that 4.
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To solve this problem, let's start constructing the pyramid step by step:
Level 1:
4
4 4
4 4 4
Level 2:
4
4 4
4 4 4
4 4 4 4
Level 3:
4
4 4
4 4 4
4 4 4 4
4 4 4 4 4
Now, we need to place ten money amounts in the pyramid to total $10,000. Let's make each row have increasing amounts of money.
Level 1:
$1,200
4 4
4 4 4
Level 2:
$1,600
$1,600
4 4 4
4 4 4 4
Level 3:
$2,200
$2,200
$2,200
4 4 4
4 4 4 4
Level 4:
$2,800
$2,800
$2,800
$2,800
4 4 4
Level 5:
$3,400
$3,400
$3,400
$3,400
$3,400
By placing the money amounts as shown above, the total amount in the pyramid is: $3,400 + $3,400 + $3,400 + $3,400 + $3,400 = $17,000.
To adjust the total to $10,000, we need to make some modifications:
Level 1:
$1,000
4 4
4 4 4
Level 2:
$1,200
$1,200
4 4 4
4 4 4 4
Level 3:
$1,400
$1,400
$1,400
4 4 4
4 4 4 4
Level 4:
$1,600
$1,600
$1,600
$1,600
4 4 4
Level 5:
$1,800
$1,800
$1,800
$1,800
$1,800
By placing the modified money amounts as shown above, the total amount in the pyramid is: $1,800 + $1,800 + $1,800 + $1,800 + $1,800 = $9,000.
To reach the desired total of $10,000, we'll add one more block with the value of $1,000:
Level 1:
$1,000
4 4
4 4 4
Level 2:
$1,200
$1,200
4 4 4
4 4 4 4
Level 3:
$1,400
$1,400
$1,400
4 4 4
4 4 4 4
Level 4:
$1,600
$1,600
$1,600
$1,600
4 4 4
Level 5:
$1,000
$1,800
$1,800
$1,800
$1,800
Now, the total amount in the pyramid is: $1,000 + $1,800 + $1,800 + $1,800 + $1,800 = $8,200. To reach the desired total of $10,000, we need to modify one of the $1,800 blocks to $1,100.
Modified pyramid:
Level 1:
$1,000
4 4
4 4 4
Level 2:
$1,200
$1,200
4 4 4
4 4 4 4
Level 3:
$1,400
$1,400
$1,400
4 4 4
4 4 4 4
Level 4:
$1,600
$1,600
$1,600
$1,600
4 4 4
Level 5:
$1,100
$1,800
$1,800
$1,800
$1,800
Now, the total amount in the pyramid is: $1,000 + $1,100 + $1,800 + $1,800 + $1,800 = $8,500.
To reach the desired total of $10,000, we need to modify one of the $1,800 blocks to $1,500.
Modified pyramid:
Level 1:
$1,000
4 4
4 4 4
Level 2:
$1,200
$1,200
4 4 4
4 4 4 4
Level 3:
$1,400
$1,400
$1,400
4 4 4
4 4 4 4
Level 4:
$1,600
$1,600
$1,600
$1,600
4 4 4
Level 5:
$1,100
$1,500
$1,800
$1,800
$1,800
Now, the total amount in the pyramid is: $1,000 + $1,100 + $1,500 + $1,800 + $1,800 = $7,200.
To reach the desired total of $10,000, we need to modify one of the $1,800 blocks to $2,800.
Modified pyramid:
Level 1:
$1,000
4 4
4 4 4
Level 2:
$1,200
$1,200
4 4 4
4 4 4 4
Level 3:
$1,400
$1,400
$1,400
4 4 4
4 4 4 4
Level 4:
$1,600
$1,600
$1,600
$1,600
4 4 4
Level 5:
$1,100
$1,500
$2,800
$1,800
$1,800
Finally, the total amount in the pyramid is: $1,000 + $1,100 + $1,500 + $2,800 + $1,800 = $8,200.
To adjust the total to $10,000, we need to modify one of the $1,000 blocks to $1,800.
Modified pyramid:
Level 1:
$1,800
4 4
4 4 4
Level 2:
$1,200
$1,200
4 4 4
4 4 4 4
Level 3:
$1,400
$1,400
$1,400
4 4 4
4 4 4 4
Level 4:
$1,600
$1,600
$1,600
$1,600
4 4 4
Level 5:
$1,100
$1,500
$2,800
$1,800
$1,800
Now, the total amount in the pyramid is: $1,800 + $1,200 + $1,200 + $1,400 + $1,400 + $1,600 + $1,600 + $1,600 + $1,800 + $1,800 = $15,600.
Since the total amount exceeds $10,000, it is not possible to place ten money amounts totaling $10,000 using only the number four in the blocks of this pyramid.
To solve this problem, we need to find ten different amounts using only the number four to calculate a total of $10,000. Here's a possible solution:
We can start by recognizing the pattern that if we multiply four by itself, we get sixteen (4 * 4 = 16). Then, if we multiply sixteen by four, we get sixty-four (16 * 4 = 64). We can continue this pattern to find the multiples of four:
4 * 4 = 16
16 * 4 = 64
64 * 4 = 256
256 * 4 = 1,024
1,024 * 4 = 4,096
4,096 * 4 = 16,384
16,384 * 4 = 65,536
65,536 * 4 = 262,144
262,144 * 4 = 1,048,576
1,048,576 * 4 = 4,194,304
Now, we have ten different amounts using only the number four. However, these amounts exceed $10,000. To adjust them, we can subtract the difference between 4,194,304 and 10,000 (4,194,304 - 10,000 = 4,184,304). We'll subtract this difference from the largest amount, 4,194,304:
4,194,304 - 4,184,304 = 10,000
Hence, the ten money amounts using only the number four to total $10,000 in the pyramid would be:
$4
$16
$64
$256
$1,024
$4,096
$16,384
$65,536
$262,144
$4,184,304
I hope this helps you find the solution!